:: GOBRD11 semantic presentation
begin
theorem
:: GOBRD11:1
for
GX
being ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
for
A
being ( ( ) ( )
Subset
of )
for
p
being ( ( ) ( )
Point
of ( ( ) ( non
empty
)
set
) ) st
p
: ( ( ) ( )
Point
of ( ( ) ( non
empty
)
set
) )
in
A
: ( ( ) ( )
Subset
of ) &
A
: ( ( ) ( )
Subset
of ) is
connected
holds
A
: ( ( ) ( )
Subset
of )
c=
Component_of
p
: ( ( ) ( )
Point
of ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD11:2
for
GX
being ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
for
A
,
B
,
C
being ( ( ) ( )
Subset
of ) st
C
: ( ( ) ( )
Subset
of ) is
a_component
&
A
: ( ( ) ( )
Subset
of )
c=
C
: ( ( ) ( )
Subset
of ) &
B
: ( ( ) ( )
Subset
of ) is
connected
&
Cl
A
: ( ( ) ( )
Subset
of ) : ( ( ) ( )
Element
of
bool
the
carrier
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
meets
Cl
B
: ( ( ) ( )
Subset
of ) : ( ( ) ( )
Element
of
bool
the
carrier
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) holds
B
: ( ( ) ( )
Subset
of )
c=
C
: ( ( ) ( )
Subset
of ) ;
theorem
:: GOBRD11:3
for
GZ
being ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
for
A
,
B
being ( ( ) ( )
Subset
of ) st
A
: ( ( ) ( )
Subset
of ) is
a_component
&
B
: ( ( ) ( )
Subset
of ) is
a_component
holds
A
: ( ( ) ( )
Subset
of )
\/
B
: ( ( ) ( )
Subset
of ) : ( ( ) ( )
Element
of
bool
the
carrier
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) is ( ( ) ( )
a_union_of_components
of
GZ
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) ) ;
theorem
:: GOBRD11:4
for
GX
being ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
for
B1
,
B2
,
V
being ( ( ) ( )
Subset
of ) holds
Down
(
(
B1
: ( ( ) ( )
Subset
of )
\/
B2
: ( ( ) ( )
Subset
of )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) ,
V
: ( ( ) ( )
Subset
of ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
|
b
4
: ( ( ) ( )
Subset
of )
)
: ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) ) : ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) )
=
(
Down
(
B1
: ( ( ) ( )
Subset
of ) ,
V
: ( ( ) ( )
Subset
of ) )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
|
b
4
: ( ( ) ( )
Subset
of )
)
: ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) ) : ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) )
\/
(
Down
(
B2
: ( ( ) ( )
Subset
of ) ,
V
: ( ( ) ( )
Subset
of ) )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
|
b
4
: ( ( ) ( )
Subset
of )
)
: ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) ) : ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
|
b
4
: ( ( ) ( )
Subset
of )
)
: ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) ) : ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD11:5
for
GX
being ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
for
B1
,
B2
,
V
being ( ( ) ( )
Subset
of ) holds
Down
(
(
B1
: ( ( ) ( )
Subset
of )
/\
B2
: ( ( ) ( )
Subset
of )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) ,
V
: ( ( ) ( )
Subset
of ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
|
b
4
: ( ( ) ( )
Subset
of )
)
: ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) ) : ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) )
=
(
Down
(
B1
: ( ( ) ( )
Subset
of ) ,
V
: ( ( ) ( )
Subset
of ) )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
|
b
4
: ( ( ) ( )
Subset
of )
)
: ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) ) : ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) )
/\
(
Down
(
B2
: ( ( ) ( )
Subset
of ) ,
V
: ( ( ) ( )
Subset
of ) )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
|
b
4
: ( ( ) ( )
Subset
of )
)
: ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) ) : ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
|
b
4
: ( ( ) ( )
Subset
of )
)
: ( (
strict
) (
strict
TopSpace-like
)
SubSpace
of
b
1
: ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
) ) : ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD11:6
for
f
being ( ( non
empty
non
constant
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
V24
() non
constant
FinSequence-like
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
L~
f
: ( ( non
empty
non
constant
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
V24
() non
constant
FinSequence-like
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
`
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
<>
{}
: ( ( ) (
empty
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
set
) ;
registration
let
f
be ( ( non
empty
non
constant
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
V24
() non
constant
FinSequence-like
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ;
cluster
(
L~
f
: ( ( non
empty
non
constant
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
V24
() non
constant
FinSequence-like
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
`
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
->
non
empty
;
end;
theorem
:: GOBRD11:7
for
f
being ( ( non
empty
non
constant
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
V24
() non
constant
FinSequence-like
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
=
union
{
(
cell
(
(
GoB
f
: ( ( non
empty
non
constant
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
V24
() non
constant
FinSequence-like
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) where
i
,
j
is ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) : (
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
len
(
GoB
f
: ( ( non
empty
non
constant
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
V24
() non
constant
FinSequence-like
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
width
(
GoB
f
: ( ( non
empty
non
constant
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
V24
() non
constant
FinSequence-like
V180
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
}
: ( ( ) ( )
set
) ;
theorem
:: GOBRD11:8
for
s1
being ( ( ) (
V14
()
real
ext-real
)
Real
)
for
P1
,
P2
being ( ( ) ( )
Subset
of ) st
P1
: ( ( ) ( )
Subset
of )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
&
P2
: ( ( ) ( )
Subset
of )
=
{
|[
r2
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s2
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r2
,
s2
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s2
: ( ( ) (
V14
()
real
ext-real
)
Real
)
>
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
holds
P1
: ( ( ) ( )
Subset
of )
=
P2
: ( ( ) ( )
Subset
of )
`
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD11:9
for
s1
being ( ( ) (
V14
()
real
ext-real
)
Real
)
for
P1
,
P2
being ( ( ) ( )
Subset
of ) st
P1
: ( ( ) ( )
Subset
of )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
>=
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
&
P2
: ( ( ) ( )
Subset
of )
=
{
|[
r2
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s2
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r2
,
s2
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s2
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
holds
P1
: ( ( ) ( )
Subset
of )
=
P2
: ( ( ) ( )
Subset
of )
`
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD11:10
for
s1
being ( ( ) (
V14
()
real
ext-real
)
Real
)
for
P1
,
P2
being ( ( ) ( )
Subset
of ) st
P1
: ( ( ) ( )
Subset
of )
=
{
|[
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
s
,
r
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
>=
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
&
P2
: ( ( ) ( )
Subset
of )
=
{
|[
s2
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
r2
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
s2
,
r2
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s2
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
holds
P1
: ( ( ) ( )
Subset
of )
=
P2
: ( ( ) ( )
Subset
of )
`
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD11:11
for
s1
being ( ( ) (
V14
()
real
ext-real
)
Real
)
for
P1
,
P2
being ( ( ) ( )
Subset
of ) st
P1
: ( ( ) ( )
Subset
of )
=
{
|[
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
s
,
r
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
&
P2
: ( ( ) ( )
Subset
of )
=
{
|[
s2
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
r2
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
s2
,
r2
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s2
: ( ( ) (
V14
()
real
ext-real
)
Real
)
>
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
holds
P1
: ( ( ) ( )
Subset
of )
=
P2
: ( ( ) ( )
Subset
of )
`
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD11:12
for
P
being ( ( ) ( )
Subset
of )
for
s1
being ( ( ) (
V14
()
real
ext-real
)
Real
) st
P
: ( ( ) ( )
Subset
of )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
holds
P
: ( ( ) ( )
Subset
of ) is
closed
;
theorem
:: GOBRD11:13
for
P
being ( ( ) ( )
Subset
of )
for
s1
being ( ( ) (
V14
()
real
ext-real
)
Real
) st
P
: ( ( ) ( )
Subset
of )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
holds
P
: ( ( ) ( )
Subset
of ) is
closed
;
theorem
:: GOBRD11:14
for
P
being ( ( ) ( )
Subset
of )
for
s1
being ( ( ) (
V14
()
real
ext-real
)
Real
) st
P
: ( ( ) ( )
Subset
of )
=
{
|[
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
s
,
r
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
holds
P
: ( ( ) ( )
Subset
of ) is
closed
;
theorem
:: GOBRD11:15
for
P
being ( ( ) ( )
Subset
of )
for
s1
being ( ( ) (
V14
()
real
ext-real
)
Real
) st
P
: ( ( ) ( )
Subset
of )
=
{
|[
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
s
,
r
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s1
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
holds
P
: ( ( ) ( )
Subset
of ) is
closed
;
theorem
:: GOBRD11:16
for
j
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
tabular
) (
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) holds
h_strip
(
G
: ( (
tabular
) (
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) is
closed
;
theorem
:: GOBRD11:17
for
j
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
tabular
) (
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) holds
v_strip
(
G
: ( (
tabular
) (
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) is
closed
;
theorem
:: GOBRD11:18
for
G
being ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) st
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) is
X_equal-in-line
holds
v_strip
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) ,
0
: ( ( ) (
empty
natural
V14
()
real
ext-real
non
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
}
;
theorem
:: GOBRD11:19
for
G
being ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) st
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) is
X_equal-in-line
holds
v_strip
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) ,
(
len
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
*
(
(
len
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
;
theorem
:: GOBRD11:20
for
i
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) st
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) is
X_equal-in-line
& 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<
len
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) holds
v_strip
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) ,
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
*
(
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
*
(
(
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) )
}
;
theorem
:: GOBRD11:21
for
G
being ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) st
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) is
Y_equal-in-column
holds
h_strip
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) ,
0
: ( ( ) (
empty
natural
V14
()
real
ext-real
non
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
}
;
theorem
:: GOBRD11:22
for
G
being ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) st
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) is
Y_equal-in-column
holds
h_strip
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) ,
(
width
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) :
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
width
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
}
;
theorem
:: GOBRD11:23
for
j
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) st
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) is
Y_equal-in-column
& 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<
width
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) holds
h_strip
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) )
}
;
theorem
:: GOBRD11:24
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) ,
0
: ( ( ) (
empty
natural
V14
()
real
ext-real
non
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
0
: ( ( ) (
empty
natural
V14
()
real
ext-real
non
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) &
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) )
}
;
theorem
:: GOBRD11:25
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) ,
0
: ( ( ) (
empty
natural
V14
()
real
ext-real
non
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) &
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) )
}
;
theorem
:: GOBRD11:26
for
j
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) st 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) ,
0
: ( ( ) (
empty
natural
V14
()
real
ext-real
non
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) &
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) )
}
;
theorem
:: GOBRD11:27
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) ,
(
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
0
: ( ( ) (
empty
natural
V14
()
real
ext-real
non
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(
(
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) )
}
;
theorem
:: GOBRD11:28
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) ,
(
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(
(
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) )
}
;
theorem
:: GOBRD11:29
for
j
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) st 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) ,
(
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(
(
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) )
}
;
theorem
:: GOBRD11:30
for
i
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) st 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) ,
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
0
: ( ( ) (
empty
natural
V14
()
real
ext-real
non
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(
(
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) &
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) )
}
;
theorem
:: GOBRD11:31
for
i
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) st 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) ,
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(
(
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) &
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) )
}
;
theorem
:: GOBRD11:32
for
i
,
j
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) st 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) & 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of ) ,
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
{
|[
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
]|
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V14
()
real
ext-real
)
Real
) : (
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
r
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
r
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(
(
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) &
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) )
<=
s
: ( ( ) (
V14
()
real
ext-real
)
Real
) &
s
: ( ( ) (
V14
()
real
ext-real
)
Real
)
<=
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
)
Matrix
of )
*
(1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
V43
(2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
V100
()
FinSequence-like
)
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V14
()
real
ext-real
)
Element
of
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) ) )
}
;
theorem
:: GOBRD11:33
for
i
,
j
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
tabular
) (
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) holds
cell
(
G
: ( (
tabular
) (
V19
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) ,
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) is
closed
;
theorem
:: GOBRD11:34
for
G
being ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) holds
( 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
len
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) & 1 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
width
G
: ( (
V21
()
tabular
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
)
Matrix
of ) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) ;
theorem
:: GOBRD11:35
for
i
,
j
being ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
len
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) &
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
<=
width
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) holds
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
=
Cl
(
Int
(
cell
(
G
: ( (
V21
()
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
V19
()
V21
()
V22
(
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
V23
(
K295
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
M12
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
V24
()
FinSequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
natural
V14
()
real
ext-real
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
bool
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
natural
V14
()
real
ext-real
positive
non
negative
V108
()
V109
()
V110
()
V111
()
V112
()
V113
()
V114
()
V115
() )
Element
of
NAT
: ( ( ) (
V110
()
V111
()
V112
()
V113
()
V114
()
V115
()
V116
() )
Element
of
bool
REAL
: ( ( ) (
V110
()
V111
()
V112
()
V116
() )
set
) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V136
()
V161
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
)
set
) ) ;