:: JORDAN5B semantic presentation

begin

theorem :: JORDAN5B:1
for i1 being ( ( natural ) ( natural V28() real ext-real ) Nat) st 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= i1 : ( ( natural ) ( natural V28() real ext-real ) Nat) holds
i1 : ( ( natural ) ( natural V28() real ext-real ) Nat) -' 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V28() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) < i1 : ( ( natural ) ( natural V28() real ext-real ) Nat) ;

theorem :: JORDAN5B:2
for i, k being ( ( natural ) ( natural V28() real ext-real ) Nat) st i : ( ( natural ) ( natural V28() real ext-real ) Nat) + 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( natural ) ( natural V28() real ext-real ) Nat) holds
1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( natural ) ( natural V28() real ext-real ) Nat) -' i : ( ( natural ) ( natural V28() real ext-real ) Nat) : ( ( ) ( natural V28() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: JORDAN5B:3
for i, k being ( ( natural ) ( natural V28() real ext-real ) Nat) st 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( natural ) ( natural V28() real ext-real ) Nat) & 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( natural ) ( natural V28() real ext-real ) Nat) holds
(k : ( ( natural ) ( natural V28() real ext-real ) Nat) -' i : ( ( natural ) ( natural V28() real ext-real ) Nat) ) : ( ( ) ( natural V28() real ext-real non negative V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= k : ( ( natural ) ( natural V28() real ext-real ) Nat) ;

theorem :: JORDAN5B:4
for r being ( ( real ) ( V28() real ext-real ) number ) st r : ( ( real ) ( V28() real ext-real ) number ) in the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) holds
1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) - r : ( ( real ) ( V28() real ext-real ) number ) : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) in the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) ;

theorem :: JORDAN5B:5
for p, q, p1 being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) <> q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) & p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in LSeg (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) = p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) `2 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) holds
p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) = p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:6
for p, q, p1 being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) <> q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) & p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in LSeg (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) = p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) `1 : ( ( ) ( V28() real ext-real ) Element of REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) holds
p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) = p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:7
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for P being ( ( non empty ) ( functional non empty ) Subset of )
for F being ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) )
for i being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq & P : ( ( non empty ) ( functional non empty ) Subset of ) = L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) is being_homeomorphism & F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) . 0 : ( ( ) ( Function-like functional empty natural V28() real ext-real non positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V51() V63() V66() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) & F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) . 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) holds
ex p1, p2 being ( ( ) ( V28() real ext-real ) Real) st
( p1 : ( ( ) ( V28() real ext-real ) Real) < p2 : ( ( ) ( V28() real ext-real ) Real) & 0 : ( ( ) ( Function-like functional empty natural V28() real ext-real non positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V51() V63() V66() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= p1 : ( ( ) ( V28() real ext-real ) Real) & p1 : ( ( ) ( V28() real ext-real ) Real) <= 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & 0 : ( ( ) ( Function-like functional empty natural V28() real ext-real non positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V51() V63() V66() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= p2 : ( ( ) ( V28() real ext-real ) Real) & p2 : ( ( ) ( V28() real ext-real ) Real) <= 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) = F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) .: [.p1 : ( ( ) ( V28() real ext-real ) Real) ,p2 : ( ( ) ( V28() real ext-real ) Real) .] : ( ( ) ( V45() V46() V47() V66() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) . p1 : ( ( ) ( V28() real ext-real ) Real) : ( ( ) ( ) set ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) & F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) . p2 : ( ( ) ( V28() real ext-real ) Real) : ( ( ) ( ) set ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. (i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ;

theorem :: JORDAN5B:8
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for Q, R being ( ( non empty ) ( functional non empty ) Subset of )
for F being ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) )
for i being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) )
for P being ( ( non empty ) ( non empty V45() V46() V47() ) Subset of ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq & F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) is being_homeomorphism & F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) . 0 : ( ( ) ( Function-like functional empty natural V28() real ext-real non positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V51() V63() V66() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) & F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) . 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) & 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) .: P : ( ( non empty ) ( non empty V45() V46() V47() ) Subset of ) : ( ( ) ( ) Element of K19( the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & Q : ( ( non empty ) ( functional non empty ) Subset of ) = L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & R : ( ( non empty ) ( functional non empty ) Subset of ) = LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
ex G being ( ( Function-like quasi_total ) ( Relation-like the carrier of (I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) | b6 : ( ( non empty ) ( non empty V45() V46() V47() ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like V145() ) SubSpace of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b3 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) st
( G : ( ( Function-like quasi_total ) ( Relation-like the carrier of (I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) | b6 : ( ( non empty ) ( non empty V45() V46() V47() ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like V145() ) SubSpace of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b3 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) = F : ( ( Function-like quasi_total ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) | P : ( ( non empty ) ( non empty V45() V46() V47() ) Subset of ) : ( ( Function-like ) ( Relation-like the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like ) Element of K19(K20( the carrier of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) : ( ( ) ( non empty V45() V46() V47() ) set ) , the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b2 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) & G : ( ( Function-like quasi_total ) ( Relation-like the carrier of (I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) | b6 : ( ( non empty ) ( non empty V45() V46() V47() ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like V145() ) SubSpace of I[01] : ( ( ) ( non empty strict TopSpace-like V145() ) TopStruct ) ) : ( ( ) ( non empty V45() V46() V47() ) set ) -defined the carrier of ((TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) | b3 : ( ( non empty ) ( functional non empty ) Subset of ) ) : ( ( strict ) ( non empty strict TopSpace-like ) SubSpace of TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) : ( ( ) ( non empty ) set ) -valued Function-like non empty total quasi_total ) Function of ( ( ) ( non empty V45() V46() V47() ) set ) , ( ( ) ( non empty ) set ) ) is being_homeomorphism ) ;

begin

theorem :: JORDAN5B:9
for p1, p2, p being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) & p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in LSeg (p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
LE p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:10
for p, p1, p2 being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) & p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in LSeg (p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
LE p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:11
for p, p1, p2 being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in LSeg (p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) holds
LE p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:12
for p1, p2, q1, q2, q3 being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) & LE q1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) & LE q2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q3 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) holds
LE q1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q3 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:13
for p, q being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) holds
LSeg (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) = { p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) where p1 is ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) : ( LE p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) & LE p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ) } ;

theorem :: JORDAN5B:14
for n being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) )
for P being ( ( ) ( functional ) Subset of )
for p1, p2 being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(b1 : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st P : ( ( ) ( functional ) Subset of ) is_an_arc_of p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(b1 : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(b1 : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) holds
P : ( ( ) ( functional ) Subset of ) is_an_arc_of p2 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(b1 : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p1 : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(b1 : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:15
for i being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) )
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for P being ( ( ) ( functional ) Subset of ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq & 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & P : ( ( ) ( functional ) Subset of ) = LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
P : ( ( ) ( functional ) Subset of ) is_an_arc_of f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. (i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ;

begin

theorem :: JORDAN5B:16
for g1 being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for i being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= len g1 : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & g1 : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq & g1 : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) in L~ (mid (g1 : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,(len g1 : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: JORDAN5B:17
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq & p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) . (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like ) set ) holds
L_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) = <*p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like special ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:18
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) . (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like ) set ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq holds
Index (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,(L_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: JORDAN5B:19
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq & p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) . (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like ) set ) holds
p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ (L_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN5B:20
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq & p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) . 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like ) set ) holds
p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ (R_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN5B:21
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is one-to-one holds
B_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) = <*p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like special ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:22
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p, q being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) . (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like ) set ) & p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) . (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like ) set ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq holds
p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ (L_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN5B:23
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p, q being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) . (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like ) set ) & p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq & not p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ (L_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ (L_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN5B:24
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p, q being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq holds
L~ (B_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN5B:25
for f being ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence)
for i, j being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) holds
(LSeg (((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * (1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * (i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) /\ (LSeg (((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * (j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * ((len (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) = {} : ( ( ) ( Function-like functional empty V45() V46() V47() V48() V49() V50() V51() V63() V66() ) set ) ;

theorem :: JORDAN5B:26
for f being ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence)
for i, j being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) st 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) holds
(LSeg (((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * ((len (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * ((len (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) /\ (LSeg (((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * ((len (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * ((len (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) = {} : ( ( ) ( Function-like functional empty V45() V46() V47() V48() V49() V50() V51() V63() V66() ) set ) ;

theorem :: JORDAN5B:27
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq holds
L_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:28
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is being_S-Seq holds
R_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:29
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. (Index (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. ((Index (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: JORDAN5B:30
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for i being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is unfolded & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is s.n.c. & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) is one-to-one & len f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) >= 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) in LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
i : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) = 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: JORDAN5B:31
for f being ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence)
for j being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) )
for P being ( ( ) ( functional ) Subset of ) st 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= width (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & P : ( ( ) ( functional ) Subset of ) = LSeg (((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * (1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * ((len (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
P : ( ( ) ( functional ) Subset of ) is_S-P_arc_joining (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * (1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,(GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * ((len (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:32
for f being ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence)
for j being ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) )
for P being ( ( ) ( functional ) Subset of ) st 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) <= len (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & P : ( ( ) ( functional ) Subset of ) = LSeg (((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * (j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,((GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * (j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( functional non empty compact V231( TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) ) ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) holds
P : ( ( ) ( functional ) Subset of ) is_S-P_arc_joining (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * (j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,(GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) * (j : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width (GoB f : ( ( non constant non empty V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like non constant non empty V12() FinSequence-like V204( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( Relation-like non empty-yielding NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) -valued Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K238( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) M12( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) )) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ;

theorem :: JORDAN5B:33
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) )
for p, q being ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) st p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) & ( Index (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) < Index (q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) or ( Index (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) = Index (q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) & LE p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. (Index (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) /. ((Index (p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V28() real ext-real V43() V44() V45() V46() V47() V48() V49() V50() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) ) ) & p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) <> q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) holds
L~ (B_Cut (f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) ,p : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) ,q : ( ( ) ( Relation-like Function-like V33() V34() V35() V69(2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like ) Point of ( ( ) ( functional non empty ) set ) ) )) : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) -valued Function-like FinSequence-like ) FinSequence of ( ( ) ( functional non empty ) set ) ) : ( ( ) ( functional ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V28() real ext-real positive non negative V43() V44() V45() V46() V47() V48() V49() V50() V61() V63() ) Element of NAT : ( ( ) ( V45() V46() V47() V48() V49() V50() V51() V63() ) Element of K19(REAL : ( ( ) ( V45() V46() V47() V51() V63() V64() V66() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like T_0 T_1 T_2 V158() V183() V184() V185() V186() V187() V188() V189() strict V257() ) RLTopStruct ) : ( ( ) ( functional non empty ) set ) ) : ( ( ) ( ) set ) ) ;