begin
theorem
for
C being ( (
being_simple_closed_curve ) ( non
empty closed connected bounded compact non
horizontal non
vertical being_simple_closed_curve )
Simple_closed_curve)
for
n,
k being ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) st
n : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
is_sufficiently_large_for C : ( (
being_simple_closed_curve ) ( non
empty closed connected bounded compact non
horizontal non
vertical being_simple_closed_curve )
Simple_closed_curve) & 1 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
<= k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) &
k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
+ 1 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
<= len (Span (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty non
constant V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() ) ( non
empty V13()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18() non
constant V26()
FinSequence-like FinSubsequence-like V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) holds
(
right_cell (
(Span (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty non
constant V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() ) ( non
empty V13()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18() non
constant V26()
FinSequence-like FinSubsequence-like V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) ,
k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(Gauge (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V26()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( )
set ) )
misses C : ( (
being_simple_closed_curve ) ( non
empty closed connected bounded compact non
horizontal non
vertical being_simple_closed_curve )
Simple_closed_curve) &
left_cell (
(Span (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty non
constant V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() ) ( non
empty V13()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18() non
constant V26()
FinSequence-like FinSubsequence-like V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) ,
k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) ,
(Gauge (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V26()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) ) : ( ( ) ( )
Element of
K6( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( )
set ) )
meets C : ( (
being_simple_closed_curve ) ( non
empty closed connected bounded compact non
horizontal non
vertical being_simple_closed_curve )
Simple_closed_curve) ) ;
theorem
for
C being ( (
being_simple_closed_curve ) ( non
empty closed connected bounded compact non
horizontal non
vertical being_simple_closed_curve )
Simple_closed_curve)
for
i,
j,
k,
n being ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) st
n : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
is_sufficiently_large_for C : ( (
being_simple_closed_curve ) ( non
empty closed connected bounded compact non
horizontal non
vertical being_simple_closed_curve )
Simple_closed_curve) & 1 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
<= k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) &
k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
<= len (Span (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty non
constant V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() ) ( non
empty V13()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18() non
constant V26()
FinSequence-like FinSubsequence-like V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) &
[i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V26()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
(Span (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty non
constant V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() ) ( non
empty V13()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18() non
constant V26()
FinSequence-like FinSubsequence-like V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V136() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V26()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
i : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) ,
j : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V136() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) holds
i : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
< len (Gauge (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V26()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) ;
theorem
for
C being ( (
being_simple_closed_curve ) ( non
empty closed connected bounded compact non
horizontal non
vertical being_simple_closed_curve )
Simple_closed_curve)
for
i,
j,
k,
n being ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) st
n : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
is_sufficiently_large_for C : ( (
being_simple_closed_curve ) ( non
empty closed connected bounded compact non
horizontal non
vertical being_simple_closed_curve )
Simple_closed_curve) & 1 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
<= k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) &
k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
<= len (Span (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty non
constant V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() ) ( non
empty V13()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18() non
constant V26()
FinSequence-like FinSubsequence-like V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) &
[i : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( )
set )
in Indices (Gauge (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V26()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) ( )
set ) &
(Span (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( non
empty non
constant V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() ) ( non
empty V13()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
V18() non
constant V26()
FinSequence-like FinSubsequence-like V180( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
special unfolded s.c.c. standard V194() )
FinSequence of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
/. k : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) : ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V136() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )
= (Gauge (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V26()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
* (
i : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) ,
j : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) ) : ( ( ) (
V33(2 : ( ( ) ( non
empty V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real positive V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) )
FinSequence-like V136() )
Element of the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) holds
j : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
< width (Gauge (C : ( ( being_simple_closed_curve ) ( non empty closed connected bounded compact non horizontal non vertical being_simple_closed_curve ) Simple_closed_curve) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() V37() ext-real V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( (
tabular ) (
V13()
V15()
V16(
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) )
V17(
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) )
V18()
V26()
FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column )
FinSequence of
K338( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) ) : ( ( ) ( non
empty V21()
FinSequence-membered )
M11( the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty V4() V5() V6() V10() V11() V12() V37() ext-real positive V97() V144() V145() V146() V147() V148() V149() ) Element of NAT : ( ( ) ( non empty V4() V5() V6() V144() V145() V146() V147() V148() V149() V150() ) Element of K6(REAL : ( ( ) ( non empty V26() V144() V145() V146() V150() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like T_0 T_1 T_2 V110()
V156()
V157()
V158()
V159()
V160()
V161()
V162()
strict add-continuous Mult-continuous )
RLTopStruct ) : ( ( ) ( non
empty V21() )
set ) )) ) : ( ( ) (
V4()
V5()
V6()
V10()
V11()
V12()
V37()
ext-real V97()
V144()
V145()
V146()
V147()
V148()
V149() )
Element of
NAT : ( ( ) ( non
empty V4()
V5()
V6()
V144()
V145()
V146()
V147()
V148()
V149()
V150() )
Element of
K6(
REAL : ( ( ) ( non
empty V26()
V144()
V145()
V146()
V150() )
set ) ) : ( ( ) ( )
set ) ) ) ;