:: JORDAN1B semantic presentation
begin
theorem
:: JORDAN1B:1
for
f
being ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) holds
(
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) is
empty
iff
Rev
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
set
) is
empty
) ;
theorem
:: JORDAN1B:2
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) )
for
i
,
j
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
not
mid
(
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) is
empty
;
theorem
:: JORDAN1B:3
for
f
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
p
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) holds
(
R_Cut
(
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
.
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
)
=
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
.
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ;
theorem
:: JORDAN1B:4
for
f
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
p
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) is
being_S-Seq
&
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) holds
(
L_Cut
(
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
.
(
len
(
L_Cut
(
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
)
=
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
.
(
len
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ;
theorem
:: JORDAN1B:5
for
P
being ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) holds
W-max
P
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) : ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
<>
E-max
P
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) : ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: JORDAN1B:6
for
i
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
len
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
(
mid
(
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
(
len
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
^
<*
(
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
/.
(
len
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
*>
: ( ( ) ( non
empty
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
constant
V31
()
V38
(1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
=
mid
(
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
f
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) ;
theorem
:: JORDAN1B:7
for
p
,
q
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) st
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
<>
q
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) &
LSeg
(
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) ,
q
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) is
vertical
holds
<*
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) ,
q
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
*>
: ( ( ) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) is
being_S-Seq
;
theorem
:: JORDAN1B:8
for
p
,
q
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) st
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
<>
q
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) &
LSeg
(
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) ,
q
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) is
horizontal
holds
<*
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) ,
q
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
*>
: ( ( ) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) is
being_S-Seq
;
theorem
:: JORDAN1B:9
for
p
,
q
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
v
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) st
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_in_the_area_of
q
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) holds
Rotate
(
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
v
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
is_in_the_area_of
q
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ;
theorem
:: JORDAN1B:10
for
p
being ( ( non
trivial
) ( non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
v
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) holds
Rotate
(
p
: ( ( non
trivial
) ( non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
v
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
is_in_the_area_of
p
: ( ( non
trivial
) ( non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ;
theorem
:: JORDAN1B:11
for
f
being ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) holds
Center
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
>=
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:12
for
f
being ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) st
len
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
>=
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
Center
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:13
for
G
being ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) holds
Center
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:14
for
f
being ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) st
len
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
>=
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
Center
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
>
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:15
for
f
being ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) st
len
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
>=
3 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
Center
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
len
f
: ( (
V18
()
Function-like
FinSequence-like
) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:16
for
E
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
Center
(
Gauge
(
E
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
=
(
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
|^
(
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
+
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:17
for
E
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) holds
E
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
c=
cell
(
(
Gauge
(
E
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
0
: ( ( ) (
empty
V6
()
V10
()
V11
()
V12
()
ext-real
non
positive
non
negative
integer
V18
()
non-empty
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
one-to-one
constant
functional
V31
()
FinSequence-like
FinSubsequence-like
FinSequence-membered
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:18
for
E
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) holds not
cell
(
(
Gauge
(
E
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
0
: ( ( ) (
empty
V6
()
V10
()
V11
()
V12
()
ext-real
non
positive
non
negative
integer
V18
()
non-empty
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
one-to-one
constant
functional
V31
()
FinSequence-like
FinSubsequence-like
FinSequence-membered
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
c=
BDD
E
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:19
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) holds
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
|[
(
(
(
W-bound
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
+
(
E-bound
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
/
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
COMPLEX
: ( ( ) (
V142
()
V148
() )
set
) ) ,
(
S-bound
(
L~
(
Cage
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V31
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
]|
: ( ( ) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: JORDAN1B:20
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) holds
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
|[
(
(
(
W-bound
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
+
(
E-bound
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
/
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
COMPLEX
: ( ( ) (
V142
()
V148
() )
set
) ) ,
(
N-bound
(
L~
(
Cage
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V31
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
)
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
]|
: ( ( ) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: JORDAN1B:21
for
G
being ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
j
,
m
,
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
p
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
cell
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
(
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) &
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
=
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) ) holds
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
=
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:22
for
G
being ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
i
,
j
,
m
,
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
p
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
cell
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) &
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
=
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) ) & not
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
=
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
=
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:23
for
G
being ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
i
,
m
,
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
p
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
cell
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) &
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
=
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) ) holds
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
=
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:24
for
G
being ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
i
,
j
,
m
,
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
p
being ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
cell
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) &
p
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) )
=
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
m
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
V12
()
ext-real
)
Element
of
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) ) & not
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
=
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
=
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:25
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
C
being ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
)
for
i
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
len
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
LSeg
(
(
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ,
(
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
meets
Upper_Arc
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) : ( ( non
empty
) ( non
empty
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:26
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
C
being ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
)
for
i
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
len
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
LSeg
(
(
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ,
(
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
meets
Lower_Arc
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) : ( ( non
empty
) ( non
empty
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:27
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
C
being ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) holds
LSeg
(
(
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ,
(
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
meets
Upper_Arc
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) : ( ( non
empty
) ( non
empty
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:28
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
C
being ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) holds
LSeg
(
(
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ,
(
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
(
Gauge
(
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
meets
Lower_Arc
C
: ( (
being_simple_closed_curve
) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Simple_closed_curve
) : ( ( non
empty
) ( non
empty
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:29
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
i
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
LSeg
(
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ,
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
meets
Upper_Arc
(
L~
(
Cage
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V31
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) : ( ( non
empty
) ( non
empty
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:30
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
i
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
LSeg
(
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ,
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
meets
Lower_Arc
(
L~
(
Cage
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V31
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) : ( ( non
empty
) ( non
empty
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:31
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) holds
LSeg
(
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ,
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
meets
Upper_Arc
(
L~
(
Cage
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V31
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) : ( ( non
empty
) ( non
empty
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:32
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) holds
LSeg
(
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ,
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
Center
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
(
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
V31
()
V38
(2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
FinSequence-like
FinSubsequence-like
V134
() )
Element
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
connected
bounded
compact
V250
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
meets
Lower_Arc
(
L~
(
Cage
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
non
trivial
V18
()
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V31
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
FinSequence
of the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) ( non
empty
connected
bounded
being_simple_closed_curve
compact
non
horizontal
non
vertical
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) : ( ( non
empty
) ( non
empty
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:33
for
G
being ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
j
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
not
cell
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
0
: ( ( ) (
empty
V6
()
V10
()
V11
()
V12
()
ext-real
non
positive
non
negative
integer
V18
()
non-empty
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
one-to-one
constant
functional
V31
()
FinSequence-like
FinSubsequence-like
FinSequence-membered
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) is
bounded
;
theorem
:: JORDAN1B:34
for
G
being ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
i
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
not
cell
(
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
(
len
G
: ( ( non
empty-yielding
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) is
bounded
;
theorem
:: JORDAN1B:35
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
j
,
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
cell
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
0
: ( ( ) (
empty
V6
()
V10
()
V11
()
V12
()
ext-real
non
positive
non
negative
integer
V18
()
non-empty
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
Function-like
one-to-one
constant
functional
V31
()
FinSequence-like
FinSubsequence-like
FinSequence-membered
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
c=
UBD
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( non
empty
connected
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:36
for
E
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
j
,
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
E
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) holds
cell
(
(
Gauge
(
E
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
(
len
(
Gauge
(
E
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
c=
UBD
E
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( non
empty
connected
)
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN1B:37
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
i
,
n
,
j
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
cell
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
c=
BDD
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) holds
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
>
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:38
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
i
,
n
,
j
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
cell
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
c=
BDD
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) holds
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
>
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:39
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
i
,
n
,
j
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
cell
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
c=
BDD
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) holds
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
width
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:40
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
i
,
n
,
j
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
cell
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
c=
BDD
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) holds
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN1B:41
for
C
being ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of )
for
n
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st ex
i
,
j
being ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) st
(
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
<=
width
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) &
cell
(
(
Gauge
(
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) )
)
: ( (
V180
() ) (
V18
() non
empty-yielding
V21
(
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
V22
(
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V31
()
FinSequence-like
FinSubsequence-like
V180
()
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K331
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) )
c=
BDD
C
: ( (
connected
compact
non
horizontal
non
vertical
) ( non
empty
connected
bounded
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( )
Element
of
bool
the
U1
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V89
()
V154
()
V155
()
V172
()
V173
()
V174
()
V175
()
V176
()
V177
()
V178
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( )
set
) ) ) holds
n
: ( ( ) (
V6
()
V10
()
V11
()
V12
()
ext-real
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) )
>=
1 : ( ( ) ( non
empty
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
integer
V76
()
V142
()
V143
()
V144
()
V145
()
V146
()
V147
() )
Element
of
NAT
: ( ( ) (
V142
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
() )
Element
of
bool
REAL
: ( ( ) (
V142
()
V143
()
V144
()
V148
() )
set
) : ( ( ) ( )
set
) ) ) ;