:: GOBRD14 semantic presentation
begin
theorem
:: GOBRD14:1
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
P
being ( ( ) ( )
Subset
of )
for
p
being ( ( ) ( )
Point
of ( ( ) ( non
empty
)
set
) ) st
p
: ( ( ) ( )
Point
of ( ( ) ( non
empty
)
set
) )
=
0.REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) &
P
: ( ( ) ( )
Subset
of )
is_outside_component_of
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) holds
ex
r
being ( ( ) (
V28
()
real
ext-real
)
Real
) st
(
r
: ( ( ) (
V28
()
real
ext-real
)
Real
)
>
0
: ( ( ) (
Function-like
functional
empty
V12
()
ordinal
natural
V28
()
real
ext-real
non
positive
non
negative
integer
FinSequence-membered
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
(
Ball
(
p
: ( ( ) ( )
Point
of ( ( ) ( non
empty
)
set
) ) ,
r
: ( ( ) (
V28
()
real
ext-real
)
Real
) )
)
: ( ( ) ( )
Element
of
K19
( the
carrier
of
(
Euclid
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
Reflexive
discerning
symmetric
triangle
) ( non
empty
strict
Reflexive
discerning
symmetric
triangle
)
MetrStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) )
`
: ( ( ) ( )
Element
of
K19
( the
carrier
of
(
Euclid
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
Reflexive
discerning
symmetric
triangle
) ( non
empty
strict
Reflexive
discerning
symmetric
triangle
)
MetrStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) )
c=
P
: ( ( ) ( )
Subset
of ) ) ;
begin
theorem
:: GOBRD14:2
for
n
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
L~
f
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
K19
( the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) )
<>
{}
: ( ( ) (
Function-like
functional
empty
V12
()
FinSequence-membered
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
set
) holds
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ;
theorem
:: GOBRD14:3
for
i
,
j
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st 1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<
len
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) & 1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<
width
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) holds
cell
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
product
(
(1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
-->
(
[.
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
`1
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ,
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
`1
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
.]
: ( ( ) (
compact
V174
()
V175
()
V176
()
real-bounded
)
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ,
[.
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
`2
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ,
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
`2
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
.]
: ( ( ) (
compact
V174
()
V175
()
V176
()
real-bounded
)
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
{
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
}
: ( ( ) ( non
empty
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
set
) ,
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) (
Relation-like
{
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
}
: ( ( ) ( non
empty
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
set
)
-defined
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V18
(
{
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
}
: ( ( ) ( non
empty
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
set
) ,
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
Element
of
K19
(
K20
(
{
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
}
: ( ( ) ( non
empty
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
set
) ,
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ;
theorem
:: GOBRD14:4
for
i
,
j
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st 1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<
len
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) & 1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<
width
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) holds
cell
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) ( )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) is
compact
;
theorem
:: GOBRD14:5
for
i
,
j
,
n
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st
[
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
]
: ( ( ) ( non
empty
)
set
)
in
Indices
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) ( )
set
) &
[
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
]
: ( ( ) ( non
empty
)
set
)
in
Indices
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) ( )
set
) holds
dist
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ,
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
=
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
`1
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
-
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
`1
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:6
for
i
,
j
,
n
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st
[
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
]
: ( ( ) ( non
empty
)
set
)
in
Indices
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) ( )
set
) &
[
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
]
: ( ( ) ( non
empty
)
set
)
in
Indices
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) ( )
set
) holds
dist
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ,
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
=
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
`2
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
-
(
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
`2
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:7
for
n
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
for
C
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) holds 3 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
(
len
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
-'
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ;
theorem
:: GOBRD14:8
for
i
,
j
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
for
C
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) st
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) holds
for
a
,
b
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) st 2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
a
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
a
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
(
len
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
-
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
integer
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) & 2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
b
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
b
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
(
len
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
-
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
integer
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) holds
ex
c
,
d
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) st
( 2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
c
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
c
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
(
len
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
-
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
integer
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) & 2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
d
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
d
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<=
(
len
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
-
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
integer
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) &
[
c
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
d
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
]
: ( ( ) ( non
empty
)
set
)
in
Indices
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) ( )
set
) &
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(
a
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
b
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
=
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(
c
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
d
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) &
c
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
=
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
(
(
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
|^
(
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
-'
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
*
(
a
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
-'
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
d
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
=
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
(
(
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
|^
(
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
-'
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
*
(
b
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
-'
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ) ;
theorem
:: GOBRD14:9
for
i
,
j
,
n
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
for
C
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) st
[
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
]
: ( ( ) ( non
empty
)
set
)
in
Indices
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) ( )
set
) &
[
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
]
: ( ( ) ( non
empty
)
set
)
in
Indices
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) ( )
set
) holds
dist
(
(
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ,
(
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
(
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
=
(
(
N-bound
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
-
(
S-bound
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
/
(
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
|^
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:10
for
i
,
j
,
n
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
for
C
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) st
[
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
]
: ( ( ) ( non
empty
)
set
)
in
Indices
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) ( )
set
) &
[
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
]
: ( ( ) ( non
empty
)
set
)
in
Indices
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) ( )
set
) holds
dist
(
(
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ,
(
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(
(
i
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
+
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,
j
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
=
(
(
E-bound
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
-
(
W-bound
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
/
(
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
|^
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:11
for
C
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
for
r
,
t
being ( (
real
) (
V28
()
real
ext-real
)
number
) st
r
: ( (
real
) (
V28
()
real
ext-real
)
number
)
>
0
: ( ( ) (
Function-like
functional
empty
V12
()
ordinal
natural
V28
()
real
ext-real
non
positive
non
negative
integer
FinSequence-membered
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
t
: ( (
real
) (
V28
()
real
ext-real
)
number
)
>
0
: ( ( ) (
Function-like
functional
empty
V12
()
ordinal
natural
V28
()
real
ext-real
non
positive
non
negative
integer
FinSequence-membered
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) holds
ex
n
being ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) st
( 1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
<
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) &
dist
(
(
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ,
(
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
<
r
: ( (
real
) (
V28
()
real
ext-real
)
number
) &
dist
(
(
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ,
(
(
Gauge
(
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
ordinal
natural
V28
()
real
ext-real
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
-valued
Function-like
V38
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
*
: ( ( ) (
functional
non
empty
FinSequence-membered
)
FinSequenceSet
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) )
*
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
<
t
: ( (
real
) (
V28
()
real
ext-real
)
number
) ) ;
begin
theorem
:: GOBRD14:12
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
P
being ( ( ) ( )
Subset
of ) holds
( not
P
: ( ( ) ( )
Subset
of ) is
a_component
or
P
: ( ( ) ( )
Subset
of )
=
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) or
P
: ( ( ) ( )
Subset
of )
=
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ;
theorem
:: GOBRD14:13
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
A1
,
A2
being ( ( ) ( )
Subset
of ) st
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
`
: ( ( ) ( non
empty
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
A1
: ( ( ) ( )
Subset
of )
\/
A2
: ( ( ) ( )
Subset
of ) : ( ( ) ( )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) &
A1
: ( ( ) ( )
Subset
of )
misses
A2
: ( ( ) ( )
Subset
of ) & ( for
C1
,
C2
being ( ( ) ( )
Subset
of ) st
C1
: ( ( ) ( )
Subset
of )
=
A1
: ( ( ) ( )
Subset
of ) &
C2
: ( ( ) ( )
Subset
of )
=
A2
: ( ( ) ( )
Subset
of ) holds
(
C1
: ( ( ) ( )
Subset
of ) is
a_component
&
C2
: ( ( ) ( )
Subset
of ) is
a_component
) ) & not (
A1
: ( ( ) ( )
Subset
of )
=
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) &
A2
: ( ( ) ( )
Subset
of )
=
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) holds
(
A1
: ( ( ) ( )
Subset
of )
=
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) &
A2
: ( ( ) ( )
Subset
of )
=
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ;
theorem
:: GOBRD14:14
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
misses
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:15
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
(
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
\/
(
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) ( non
empty
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
\/
(
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ;
theorem
:: GOBRD14:16
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
p
being ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) ) holds
(
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) iff ( not
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) & not
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ) ;
theorem
:: GOBRD14:17
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
p
being ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) ) holds
(
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) iff ( not
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) & not
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ) ;
theorem
:: GOBRD14:18
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
p
being ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) ) holds
(
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) iff ( not
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) & not
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ) ;
theorem
:: GOBRD14:19
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
(
Cl
(
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
closed
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
\
(
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:20
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
(
Cl
(
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
closed
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
\
(
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:21
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
Cl
(
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
(
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
\/
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:22
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
Cl
(
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
(
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
\/
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
registration
let
f
be ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ;
cluster
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
->
Jordan
;
end;
theorem
:: GOBRD14:23
for
p
being ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) holds
W-bound
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
<
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
`1
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:24
for
p
being ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) holds
E-bound
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
>
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
`1
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:25
for
p
being ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) holds
N-bound
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
>
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
`2
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:26
for
p
being ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) holds
S-bound
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
<
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
`2
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:27
for
p
,
q
being ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) st
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) &
q
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) )
in
LeftComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) holds
LSeg
(
p
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) ) ,
q
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
Function-like
V38
()
V45
(2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
FinSequence-like
FinSubsequence-like
V166
() )
Point
of ( ( ) ( non
empty
V12
() )
set
) ) ) : ( ( ) (
boundary
connected
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
meets
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:28
for
C
being ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of ) holds
Cl
(
RightComp
(
SpStSeq
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
rectangular
clockwise_oriented
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
product
(
(1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) )
-->
(
[.
(
W-bound
(
L~
(
SpStSeq
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
rectangular
clockwise_oriented
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ,
(
E-bound
(
L~
(
SpStSeq
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
rectangular
clockwise_oriented
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
.]
: ( ( ) (
compact
V174
()
V175
()
V176
()
real-bounded
)
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ,
[.
(
S-bound
(
L~
(
SpStSeq
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
rectangular
clockwise_oriented
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ,
(
N-bound
(
L~
(
SpStSeq
C
: ( (
compact
non
horizontal
non
vertical
) ( non
empty
compact
bounded
non
horizontal
non
vertical
)
Subset
of )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
rectangular
clockwise_oriented
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) )
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
.]
: ( ( ) (
compact
V174
()
V175
()
V176
()
real-bounded
)
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
{
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
}
: ( ( ) ( non
empty
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
set
) ,
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) (
Relation-like
{
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
}
: ( ( ) ( non
empty
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
set
)
-defined
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V18
(
{
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
}
: ( ( ) ( non
empty
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
set
) ,
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
Element
of
K19
(
K20
(
{
1 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) ,2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
}
: ( ( ) ( non
empty
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
set
) ,
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ;
theorem
:: GOBRD14:29
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
proj1
: ( (
Function-like
V18
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-defined
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
)
-valued
Function-like
V18
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
V229
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
(
K20
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) )
.:
(
Cl
(
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
closed
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V174
()
V175
()
V176
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
proj1
: ( (
Function-like
V18
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-defined
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
)
-valued
Function-like
V18
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
V229
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
(
K20
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) )
.:
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V174
()
V175
()
V176
()
bounded_below
bounded_above
)
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:30
for
f
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
proj2
: ( (
Function-like
V18
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-defined
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
)
-valued
Function-like
V18
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
V229
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
(
K20
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) )
.:
(
Cl
(
RightComp
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
closed
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V174
()
V175
()
V176
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
proj2
: ( (
Function-like
V18
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-defined
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
)
-valued
Function-like
V18
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
V229
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
(
K20
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ,
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
)
set
) )
.:
(
L~
f
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V174
()
V175
()
V176
()
bounded_below
bounded_above
)
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:31
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
RightComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
c=
RightComp
(
SpStSeq
(
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
rectangular
clockwise_oriented
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:32
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
Cl
(
RightComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) is
compact
;
theorem
:: GOBRD14:33
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds not
LeftComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) is
bounded
;
theorem
:: GOBRD14:34
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
LeftComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
is_outside_component_of
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:35
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
RightComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
is_inside_component_of
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:36
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
UBD
(
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
connected
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
LeftComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:37
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
BDD
(
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
=
RightComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:38
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
for
P
being ( ( ) ( )
Subset
of ) st
P
: ( ( ) ( )
Subset
of )
is_outside_component_of
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) holds
P
: ( ( ) ( )
Subset
of )
=
LeftComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:39
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
for
P
being ( ( ) ( )
Subset
of ) st
P
: ( ( ) ( )
Subset
of )
is_inside_component_of
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) holds
P
: ( ( ) ( )
Subset
of )
meets
RightComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:40
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
for
P
being ( ( ) ( )
Subset
of ) st
P
: ( ( ) ( )
Subset
of )
is_inside_component_of
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) holds
P
: ( ( ) ( )
Subset
of )
=
BDD
(
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: GOBRD14:41
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
W-bound
(
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
=
W-bound
(
RightComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:42
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
E-bound
(
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
=
E-bound
(
RightComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:43
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
N-bound
(
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
=
N-bound
(
RightComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;
theorem
:: GOBRD14:44
for
g
being ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) holds
S-bound
(
L~
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
boundary
compact
bounded
non
horizontal
non
vertical
Jordan
)
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) )
=
S-bound
(
RightComp
g
: ( ( non
constant
non
empty
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
) (
Relation-like
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
)
-valued
Function-like
non
constant
non
empty
V12
()
V38
()
FinSequence-like
FinSubsequence-like
circular
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
open
connected
V222
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) ) : ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) ) )
Element
of
K19
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
ordinal
natural
V28
()
real
ext-real
positive
non
negative
integer
V108
()
V174
()
V175
()
V176
()
V177
()
V178
()
V179
() )
Element
of
NAT
: ( ( ) (
V174
()
V175
()
V176
()
V177
()
V178
()
V179
()
V180
() )
Element
of
K19
(
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) )
)
: ( (
strict
) ( non
empty
V55
()
TopSpace-like
V121
()
V186
()
V187
()
V204
()
V205
()
V206
()
V207
()
V208
()
V209
()
V210
()
strict
add-continuous
Mult-continuous
)
RLTopStruct
) : ( ( ) ( non
empty
V12
() )
set
) ) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V38
()
V174
()
V175
()
V176
()
V180
() )
set
) ) ;