begin
theorem
for
i,
m,
k,
j being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
for
C being ( (
compact non
horizontal non
vertical ) ( non
empty functional closed bounded compact non
horizontal non
vertical )
Subset of ) st
m : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
> k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) &
[i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( )
Element of
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ,
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V23(
RAT : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V161()
V164() )
set ) )
V23(
INT : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V161()
V162()
V164() )
set ) )
V148()
V149()
V150()
V151() )
set ) )
in Indices (Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V19() non
empty-yielding V22(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
V23(
K285( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K285( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )) ) : ( ( ) ( )
set ) &
[i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( )
Element of
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ,
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V23(
RAT : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V161()
V164() )
set ) )
V23(
INT : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V161()
V162()
V164() )
set ) )
V148()
V149()
V150()
V151() )
set ) )
in Indices (Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V19() non
empty-yielding V22(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
V23(
K285( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K285( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )) ) : ( ( ) ( )
set ) holds
dist (
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) )
< dist (
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) ;
theorem
for
m,
k being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
for
C being ( (
compact non
horizontal non
vertical ) ( non
empty functional closed bounded compact non
horizontal non
vertical )
Subset of ) st
m : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
> k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) holds
dist (
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) )
< dist (
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) ;
theorem
for
i,
m,
k,
j being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
for
C being ( (
compact non
horizontal non
vertical ) ( non
empty functional closed bounded compact non
horizontal non
vertical )
Subset of ) st
m : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
> k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) &
[i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( )
Element of
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ,
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V23(
RAT : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V161()
V164() )
set ) )
V23(
INT : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V161()
V162()
V164() )
set ) )
V148()
V149()
V150()
V151() )
set ) )
in Indices (Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V19() non
empty-yielding V22(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
V23(
K285( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K285( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )) ) : ( ( ) ( )
set ) &
[(i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( )
Element of
K7(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ,
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V23(
RAT : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V161()
V164() )
set ) )
V23(
INT : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V161()
V162()
V164() )
set ) )
V148()
V149()
V150()
V151() )
set ) )
in Indices (Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V19() non
empty-yielding V22(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
V23(
K285( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )) )
Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K285( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
M9( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )) ) : ( ( ) ( )
set ) holds
dist (
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) )
< dist (
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) ;
theorem
for
m,
k being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
for
C being ( (
compact non
horizontal non
vertical ) ( non
empty functional closed bounded compact non
horizontal non
vertical )
Subset of ) st
m : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
> k : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) holds
dist (
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,m : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) )
< dist (
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( compact non horizontal non vertical ) ( non empty functional closed bounded compact non horizontal non vertical ) Subset of ) ,k : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) ;
theorem
for
C being ( (
being_simple_closed_curve ) ( non
empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non
horizontal non
vertical )
Simple_closed_curve)
for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
for
r,
t being ( (
real ) (
V11()
real ext-real )
number ) st
r : ( (
real ) (
V11()
real ext-real )
number )
> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative Function-like functional V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) &
t : ( (
real ) (
V11()
real ext-real )
number )
> 0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative Function-like functional V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) holds
ex
n being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) st
(
i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
< n : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) &
dist (
((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) )
< r : ( (
real ) (
V11()
real ext-real )
number ) &
dist (
((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ,
((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * (2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) )
< t : ( (
real ) (
V11()
real ext-real )
number ) ) ;
theorem
for
C being ( (
being_simple_closed_curve ) ( non
empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non
horizontal non
vertical )
Simple_closed_curve)
for
n being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) st
0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative Function-like functional V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
< n : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) holds
upper_bound (proj2 : ( ( Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) ( V19() V22( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) V23( REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) V148() V149() V150() ) Element of K6(K7( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ,REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( V148() V149() V150() ) set ) ) : ( ( ) ( ) set ) ) .: ((L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) /\ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() Function-like V41(2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() V149() V150() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,(len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() Function-like V41(2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() V149() V150() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact convex ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) (
V158()
V159()
V160() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) )
= upper_bound (proj2 : ( ( Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) ( V19() V22( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) V23( REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) V148() V149() V150() ) Element of K6(K7( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ,REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( V148() V149() V150() ) set ) ) : ( ( ) ( ) set ) ) .: ((L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) /\ (Vertical_Line (((E-bound (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) + (W-bound (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) / 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real ) Element of COMPLEX : ( ( ) ( non empty V34() V158() V164() ) set ) ) ) : ( ( ) ( functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) (
V158()
V159()
V160() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) ;
theorem
for
C being ( (
being_simple_closed_curve ) ( non
empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non
horizontal non
vertical )
Simple_closed_curve)
for
n being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) st
0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative Function-like functional V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
< n : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) holds
lower_bound (proj2 : ( ( Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) ( V19() V22( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) V23( REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) V148() V149() V150() ) Element of K6(K7( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ,REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( V148() V149() V150() ) set ) ) : ( ( ) ( ) set ) ) .: ((L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) /\ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() Function-like V41(2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() V149() V150() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,(len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() Function-like V41(2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() V149() V150() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact convex ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) (
V158()
V159()
V160() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) )
= lower_bound (proj2 : ( ( Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) ( V19() V22( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) V23( REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) V148() V149() V150() ) Element of K6(K7( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ,REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( V148() V149() V150() ) set ) ) : ( ( ) ( ) set ) ) .: ((L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) /\ (Vertical_Line (((E-bound (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) + (W-bound (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) / 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real ) Element of COMPLEX : ( ( ) ( non empty V34() V158() V164() ) set ) ) ) : ( ( ) ( functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) (
V158()
V159()
V160() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
V11()
real ext-real )
Element of
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) ;
theorem
for
C being ( (
being_simple_closed_curve ) ( non
empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non
horizontal non
vertical )
Simple_closed_curve)
for
n being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) st
0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative Function-like functional V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
< n : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) holds
UMP (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non
empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non
horizontal non
vertical )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )
= |[(((E-bound (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) + (W-bound (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) / 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real ) Element of COMPLEX : ( ( ) ( non empty V34() V158() V164() ) set ) ) ,(upper_bound (proj2 : ( ( Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) ( V19() V22( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) V23( REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) V148() V149() V150() ) Element of K6(K7( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ,REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( V148() V149() V150() ) set ) ) : ( ( ) ( ) set ) ) .: ((L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) /\ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() Function-like V41(2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() V149() V150() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,(len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() Function-like V41(2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() V149() V150() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact convex ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V158() V159() V160() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ]| : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ;
theorem
for
C being ( (
being_simple_closed_curve ) ( non
empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non
horizontal non
vertical )
Simple_closed_curve)
for
n being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) st
0 : ( ( ) (
empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11()
real ext-real non
positive non
negative Function-like functional V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) )
< n : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) holds
LMP (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non
empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non
horizontal non
vertical )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) : ( ( ) ( )
set ) ) : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) )
= |[(((E-bound (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) + (W-bound (L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) / 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real ) Element of COMPLEX : ( ( ) ( non empty V34() V158() V164() ) set ) ) ,(lower_bound (proj2 : ( ( Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ) ( V19() V22( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) V23( REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) Function-like V46( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) , REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) V148() V149() V150() ) Element of K6(K7( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ,REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( V148() V149() V150() ) set ) ) : ( ( ) ( ) set ) ) .: ((L~ (Cage (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non empty non constant circular special unfolded s.c.c. standard V272() ) ( non empty V2() V19() V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) Function-like non constant FinSequence-like circular special unfolded s.c.c. standard V272() ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ) : ( ( ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) /\ (LSeg (((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() Function-like V41(2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() V149() V150() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) ,((Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) * ((Center (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ,(len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty functional closed connected bounded being_simple_closed_curve compact with_the_max_arc non horizontal non vertical ) Simple_closed_curve) ,n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( tabular ) ( V19() non empty-yielding V22( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) V23(K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) Function-like FinSequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K285( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) M9( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) )) ) ) : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V19() Function-like V41(2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() V149() V150() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) )) : ( ( ) ( non empty functional closed connected bounded compact convex ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( functional ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V69() TopSpace-like T_2 V105() V171() V203() V204() V205() V206() V207() V208() V209() strict add-continuous Mult-continuous ) RLTopStruct ) : ( ( ) ( non empty V2() functional ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V158() V159() V160() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) ]| : ( ( ) (
V19()
Function-like V41(2 : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal natural V11()
real ext-real positive non
negative V32()
V49()
V158()
V159()
V160()
V161()
V162()
V163() )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal V158()
V159()
V160()
V161()
V162()
V163()
V164() )
Element of
K6(
REAL : ( ( ) ( non
empty V34()
V158()
V159()
V160()
V164() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V148()
V149()
V150() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V32() V49() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal V158() V159() V160() V161() V162() V163() V164() ) Element of K6(REAL : ( ( ) ( non empty V34() V158() V159() V160() V164() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty V69()
TopSpace-like T_2 V105()
V171()
V203()
V204()
V205()
V206()
V207()
V208()
V209()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V2()
functional )
set ) ) ;
begin