begin
theorem
for
k,
n,
i,
j being ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
for
C being ( (
connected compact non
horizontal non
vertical ) ( non
empty V21()
closed connected bounded compact non
horizontal non
vertical )
Subset of ) st 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= len (Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
[i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ,j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
[i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ,(j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
(Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
i : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
j : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) &
(Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. (k : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
i : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
(j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) holds
i : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
< len (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ;
theorem
for
k,
n,
i,
j being ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
for
C being ( (
connected compact non
horizontal non
vertical ) ( non
empty V21()
closed connected bounded compact non
horizontal non
vertical )
Subset of ) st 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= len (Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
[i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ,j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
[i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ,(j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
(Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
i : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
(j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) &
(Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. (k : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
i : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
j : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) holds
i : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
> 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ;
theorem
for
k,
n,
i,
j being ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
for
C being ( (
connected compact non
horizontal non
vertical ) ( non
empty V21()
closed connected bounded compact non
horizontal non
vertical )
Subset of ) st 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= len (Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
[i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ,j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
[(i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ,j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
(Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
i : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
j : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) &
(Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. (k : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
(i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
j : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) holds
j : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
> 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ;
theorem
for
k,
n,
i,
j being ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
for
C being ( (
connected compact non
horizontal non
vertical ) ( non
empty V21()
closed connected bounded compact non
horizontal non
vertical )
Subset of ) st 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
+ 1 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
<= len (Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) &
[i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ,j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
[(i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ,j : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
(Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. k : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
(i : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
j : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) &
(Cage (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( ( non
empty V20()
V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() ) ( non
empty non
trivial V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18()
V20()
V28()
FinSequence-like FinSubsequence-like V208( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V226() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. (k : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) + 1 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
i : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ,
j : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) (
V13()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V18()
V28()
V35(2 : ( ( ) ( non
empty V10()
V11()
V12()
V26()
ext-real positive non
negative V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like FinSubsequence-like V142() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) holds
j : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
< width (Gauge (C : ( ( connected compact non horizontal non vertical ) ( non empty V21() closed connected bounded compact non horizontal non vertical ) Subset of ) ,n : ( ( ) ( V10() V11() V12() V26() ext-real V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) )
V17(
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V28()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K324( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V10() V11() V12() V26() ext-real positive non negative V103() V150() V151() V152() V153() V154() V155() ) Element of NAT : ( ( ) ( V150() V151() V152() V153() V154() V155() V156() ) Element of K6(REAL : ( ( ) ( V150() V151() V152() V156() ) set ) ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V116()
V162()
V163()
V164()
V165()
V166()
V167()
V168()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) (
V10()
V11()
V12()
V26()
ext-real V103()
V150()
V151()
V152()
V153()
V154()
V155() )
Element of
NAT : ( ( ) (
V150()
V151()
V152()
V153()
V154()
V155()
V156() )
Element of
K6(
REAL : ( ( ) (
V150()
V151()
V152()
V156() )
set ) ) : ( ( ) ( non
empty )
set ) ) ) ;