:: GOBOARD9 semantic presentation
begin
theorem
:: GOBOARD9:1
for
GX
being ( (
TopSpace-like
) (
TopSpace-like
)
TopSpace
)
for
A1
,
A2
,
B
being ( ( ) ( )
Subset
of ) st
A1
: ( ( ) ( )
Subset
of )
is_a_component_of
B
: ( ( ) ( )
Subset
of ) &
A2
: ( ( ) ( )
Subset
of )
is_a_component_of
B
: ( ( ) ( )
Subset
of ) & not
A1
: ( ( ) ( )
Subset
of )
=
A2
: ( ( ) ( )
Subset
of ) holds
A1
: ( ( ) ( )
Subset
of )
misses
A2
: ( ( ) ( )
Subset
of ) ;
theorem
:: GOBOARD9:2
for
GX
being ( (
TopSpace-like
) (
TopSpace-like
)
TopSpace
)
for
A
,
B
being ( ( ) ( )
Subset
of )
for
AA
being ( ( ) ( )
Subset
of ) st
A
: ( ( ) ( )
Subset
of )
=
AA
: ( ( ) ( )
Subset
of ) holds
GX
: ( (
TopSpace-like
) (
TopSpace-like
)
TopSpace
)
|
A
: ( ( ) ( )
Subset
of ) : ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( (
TopSpace-like
) (
TopSpace-like
)
TopSpace
) )
=
(
GX
: ( (
TopSpace-like
) (
TopSpace-like
)
TopSpace
)
|
B
: ( ( ) ( )
Subset
of )
)
: ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( (
TopSpace-like
) (
TopSpace-like
)
TopSpace
) )
|
AA
: ( ( ) ( )
Subset
of ) : ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( (
TopSpace-like
) (
TopSpace-like
)
TopSpace
)
|
b
3
: ( ( ) ( )
Subset
of ) : ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( (
TopSpace-like
) (
TopSpace-like
)
TopSpace
) ) ) ;
theorem
:: GOBOARD9:3
for
GX
being ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
for
A
,
B
being ( ( non
empty
) ( non
empty
)
Subset
of ) st
A
: ( ( non
empty
) ( non
empty
)
Subset
of )
c=
B
: ( ( non
empty
) ( non
empty
)
Subset
of ) &
A
: ( ( non
empty
) ( non
empty
)
Subset
of ) is
connected
holds
ex
C
being ( ( ) ( )
Subset
of ) st
(
C
: ( ( ) ( )
Subset
of )
is_a_component_of
B
: ( ( non
empty
) ( non
empty
)
Subset
of ) &
A
: ( ( non
empty
) ( non
empty
)
Subset
of )
c=
C
: ( ( ) ( )
Subset
of ) ) ;
theorem
:: GOBOARD9:4
for
GX
being ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
for
A
,
B
,
C
,
D
being ( ( ) ( )
Subset
of ) st
B
: ( ( ) ( )
Subset
of ) is
connected
&
C
: ( ( ) ( )
Subset
of )
is_a_component_of
D
: ( ( ) ( )
Subset
of ) &
A
: ( ( ) ( )
Subset
of )
c=
C
: ( ( ) ( )
Subset
of ) &
A
: ( ( ) ( )
Subset
of )
meets
B
: ( ( ) ( )
Subset
of ) &
B
: ( ( ) ( )
Subset
of )
c=
D
: ( ( ) ( )
Subset
of ) holds
B
: ( ( ) ( )
Subset
of )
c=
C
: ( ( ) ( )
Subset
of ) ;
registration
cluster
non
empty
convex
for ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ;
end;
theorem
:: GOBOARD9:5
canceled;
theorem
:: GOBOARD9:6
for
P
,
Q
being ( (
convex
) (
connected
convex
)
Subset
of ) holds
P
: ( (
convex
) (
connected
convex
)
Subset
of )
/\
Q
: ( (
convex
) (
connected
convex
)
Subset
of ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
convex
;
theorem
:: GOBOARD9:7
for
f
being ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) holds
Rev
(
X_axis
f
: ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) )
=
X_axis
(
Rev
f
: ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) ;
theorem
:: GOBOARD9:8
for
f
being ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) holds
Rev
(
Y_axis
f
: ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) )
=
Y_axis
(
Rev
f
: ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) ;
registration
cluster
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
for ( ( ) ( )
set
) ;
end;
registration
let
f
be ( (
V13
()
Function-like
non
constant
FinSequence-like
) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
) ;
cluster
Rev
f
: ( (
V13
()
Function-like
non
constant
FinSequence-like
) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
)
set
) : ( (
V13
()
Function-like
FinSequence-like
) (
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
set
)
->
V13
()
Function-like
non
constant
FinSequence-like
;
end;
definition
let
f
be ( ( non
empty
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ;
:: original:
Rev
redefine
func
Rev
f
->
( ( non
empty
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ;
end;
theorem
:: GOBOARD9:9
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
,
j
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
>=
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
>=
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
+
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
=
len
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
left_cell
(
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
=
right_cell
(
(
Rev
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( non
empty
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ;
theorem
:: GOBOARD9:10
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
,
j
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
>=
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
>=
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
+
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
=
len
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
left_cell
(
(
Rev
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( non
empty
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
=
right_cell
(
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ;
theorem
:: GOBOARD9:11
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
k
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
ex
i
,
j
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
cell
(
(
GoB
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
=
left_cell
(
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: GOBOARD9:12
for
j
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
h_strip
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
convex
;
theorem
:: GOBOARD9:13
for
i
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
v_strip
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
convex
;
theorem
:: GOBOARD9:14
for
i
,
j
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
cell
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
<>
{}
: ( ( ) ( )
set
) ;
theorem
:: GOBOARD9:15
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
k
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
left_cell
(
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
<>
{}
: ( ( ) ( )
set
) ;
theorem
:: GOBOARD9:16
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
k
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
right_cell
(
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
<>
{}
: ( ( ) ( )
set
) ;
theorem
:: GOBOARD9:17
for
i
,
j
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
cell
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
convex
;
theorem
:: GOBOARD9:18
canceled;
theorem
:: GOBOARD9:19
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
k
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
left_cell
(
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
convex
;
theorem
:: GOBOARD9:20
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
k
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
right_cell
(
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
convex
;
definition
let
f
be ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ;
func
LeftComp
f
->
( ( ) ( )
Subset
of )
means
:: GOBOARD9:def 1
(
it
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopStruct
)
is_a_component_of
(
L~
f
: ( ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
add-continuous
Mult-continuous
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
add-continuous
Mult-continuous
)
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
`
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
Int
(
left_cell
(
f
: ( ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
add-continuous
Mult-continuous
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
add-continuous
Mult-continuous
)
RLTopStruct
) ,1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
c=
it
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopStruct
) );
func
RightComp
f
->
( ( ) ( )
Subset
of )
means
:: GOBOARD9:def 2
(
it
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopStruct
)
is_a_component_of
(
L~
f
: ( ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
add-continuous
Mult-continuous
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
add-continuous
Mult-continuous
)
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
`
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
Int
(
right_cell
(
f
: ( ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
add-continuous
Mult-continuous
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
add-continuous
Mult-continuous
)
RLTopStruct
) ,1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
c=
it
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopStruct
) );
end;
theorem
:: GOBOARD9:21
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
k
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
left_cell
(
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
c=
LeftComp
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( )
Subset
of ) ;
theorem
:: GOBOARD9:22
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
GoB
(
Rev
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( non
empty
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( (
tabular
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
=
GoB
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( (
tabular
) (
V13
() non
empty-yielding
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
(
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K247
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ;
theorem
:: GOBOARD9:23
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
RightComp
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( )
Subset
of )
=
LeftComp
(
Rev
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( non
empty
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( )
Subset
of ) ;
theorem
:: GOBOARD9:24
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
RightComp
(
Rev
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( non
empty
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( )
Subset
of )
=
LeftComp
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( )
Subset
of ) ;
theorem
:: GOBOARD9:25
for
f
being ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
k
being ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
right_cell
(
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
c=
RightComp
f
: ( ( non
empty
non
constant
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V13
()
V16
(
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
V17
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V174
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
V4
()
V5
()
V6
()
V10
()
V11
()
V12
()
ext-real
positive
non
negative
V90
()
V91
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
() )
Element
of
NAT
: ( ( ) ( non
empty
V4
()
V5
()
V6
()
V92
()
V93
()
V94
()
V95
()
V96
()
V97
()
V98
() )
Element
of
K6
(
REAL
: ( ( ) ( non
empty
V26
()
V92
()
V93
()
V94
()
V98
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V130
()
V155
()
V156
()
V157
()
V158
()
V159
()
V160
()
V161
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( )
Subset
of ) ;