:: JORDAN15 semantic presentation

begin

theorem :: JORDAN15:1
for A, B being ( ( ) ( functional ) Subset of ) st A : ( ( ) ( functional ) Subset of ) meets B : ( ( ) ( functional ) Subset of ) holds
proj1 : ( ( Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) ) ( V19() V22( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) V23( REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) V205( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6(K7( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ,REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) .: A : ( ( ) ( functional ) Subset of ) : ( ( ) ( V168() V169() V170() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) meets proj1 : ( ( Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) ) ( V19() V22( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) V23( REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) V205( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6(K7( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ,REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) .: B : ( ( ) ( functional ) Subset of ) : ( ( ) ( V168() V169() V170() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:2
for A, B being ( ( ) ( functional ) Subset of )
for s being ( ( real ) ( real ) number ) st A : ( ( ) ( functional ) Subset of ) misses B : ( ( ) ( functional ) Subset of ) & A : ( ( ) ( functional ) Subset of ) c= Horizontal_Line s : ( ( real ) ( real ) number ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & B : ( ( ) ( functional ) Subset of ) c= Horizontal_Line s : ( ( real ) ( real ) number ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
proj1 : ( ( Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) ) ( V19() V22( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) V23( REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) V205( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6(K7( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ,REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) .: A : ( ( ) ( functional ) Subset of ) : ( ( ) ( V168() V169() V170() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) misses proj1 : ( ( Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) ) ( V19() V22( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) V23( REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) V205( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6(K7( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ,REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) .: B : ( ( ) ( functional ) Subset of ) : ( ( ) ( V168() V169() V170() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:3
for S being ( ( closed ) ( functional closed ) Subset of ) st S : ( ( closed ) ( functional closed ) Subset of ) is bounded holds
proj1 : ( ( Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) ) ( V19() V22( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) V23( REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) V205( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6(K7( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ,REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) .: S : ( ( closed ) ( functional closed ) Subset of ) : ( ( ) ( V168() V169() V170() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) is closed ;

theorem :: JORDAN15:4
for S being ( ( compact ) ( functional closed bounded compact ) Subset of ) holds proj1 : ( ( Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) ) ( V19() V22( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) V23( REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) Function-like V46( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) , REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) V205( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6(K7( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ,REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) .: S : ( ( compact ) ( functional closed bounded compact ) Subset of ) : ( ( ) ( V168() V169() V170() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) is compact ;

theorem :: JORDAN15:5
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board)
for i, j, k, j1, k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) c= LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:6
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board)
for i, j, k, j1, k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) c= LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:7
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board)
for j, k, j1, k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((Center G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((Center G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) c= LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((Center G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((Center G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:8
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) = width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) holds
for j, k, j1, k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) c= LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:9
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex j1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:10
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:11
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex j1, k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:12
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex j1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:13
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:14
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex j1, k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:15
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex j1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:16
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:17
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex j1, k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:18
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex j1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:19
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:20
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
ex j1, k1 being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st
( j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & (LSeg (((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) ) ;

theorem :: JORDAN15:21
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:22
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:23
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) > 0 : ( ( ) ( empty ordinal natural V11() real ext-real non positive non negative Function-like functional FinSequence-membered V43() V49() V168() V169() V170() V171() V172() V173() V174() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:24
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) > 0 : ( ( ) ( empty ordinal natural V11() real ext-real non positive non negative Function-like functional FinSequence-membered V43() V49() V168() V169() V170() V171() V172() V173() V174() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:25
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:26
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:27
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of )
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( connected compact non horizontal non vertical ) ( non empty functional closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <> k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: JORDAN15:28
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:29
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:30
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:31
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:32
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) > 0 : ( ( ) ( empty ordinal natural V11() real ext-real non positive non negative Function-like functional FinSequence-membered V43() V49() V168() V169() V170() V171() V172() V173() V174() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:33
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) > 0 : ( ( ) ( empty ordinal natural V11() real ext-real non positive non negative Function-like functional FinSequence-membered V43() V49() V168() V169() V170() V171() V172() V173() V174() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:34
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:35
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:36
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:37
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:38
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:39
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:40
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) > 0 : ( ( ) ( empty ordinal natural V11() real ext-real non positive non negative Function-like functional FinSequence-membered V43() V49() V168() V169() V170() V171() V172() V173() V174() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:41
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) > 0 : ( ( ) ( empty ordinal natural V11() real ext-real non positive non negative Function-like functional FinSequence-membered V43() V49() V168() V169() V170() V171() V172() V173() V174() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:42
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:43
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,(Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:44
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i1, i2, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & ((LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & ((LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) holds
(LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:45
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i1, i2, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & ((LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & ((LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) holds
(LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:46
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i1, i2, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & ((LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & ((LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) holds
(LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:47
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i1, i2, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & ((LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Upper_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) & ((LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ (Lower_Seq (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed bounded compact ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) = {((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) } : ( ( ) ( non empty functional ) set ) holds
(LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:48
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i1, i2, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
(LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:49
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i1, i2, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
(LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i2 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i1 : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:50
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
(LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Upper_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN15:51
for n being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) )
for C being ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve)
for i, j, k being ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) < len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Upper_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) & (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) in Lower_Arc (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard clockwise_oriented ) ( non empty non trivial V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) Function-like non constant V32() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard clockwise_oriented ) FinSequence of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) holds
(LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) ) : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) ,(n : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) Function-like V32() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K295( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( non empty functional FinSequence-membered ) M9( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) )) ) * (i : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ordinal natural V11() real ext-real non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() V22( NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) Function-like V32() V39(2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V160() ) Element of the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact V264( TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) ) ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) meets Lower_Arc C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact non horizontal non vertical ) Simple_closed_curve) : ( ( non empty ) ( non empty functional ) Element of K6( the U1 of (TOP-REAL 2 : ( ( ) ( non empty ordinal natural V11() real ext-real positive non negative V43() V49() V168() V169() V170() V171() V172() V173() ) Element of NAT : ( ( ) ( V168() V169() V170() V171() V172() V173() V174() V266() ) Element of K6(REAL : ( ( ) ( non empty V32() V168() V169() V170() V174() V266() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty non trivial TopSpace-like T_2 V105() V130() V131() V132() V133() V134() V135() V136() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty non trivial functional ) set ) ) : ( ( ) ( ) set ) ) ;