:: JORDAN9 semantic presentation
begin
theorem
:: JORDAN9:1
for
T
being ( ( non
empty
TopSpace-like
) ( non
empty
TopSpace-like
)
TopSpace
)
for
B
,
C1
,
C2
,
D
being ( ( ) ( )
Subset
of ) st
B
: ( ( ) ( )
Subset
of ) is
connected
&
C1
: ( ( ) ( )
Subset
of )
is_a_component_of
D
: ( ( ) ( )
Subset
of ) &
C2
: ( ( ) ( )
Subset
of )
is_a_component_of
D
: ( ( ) ( )
Subset
of ) &
B
: ( ( ) ( )
Subset
of )
meets
C1
: ( ( ) ( )
Subset
of ) &
B
: ( ( ) ( )
Subset
of )
meets
C2
: ( ( ) ( )
Subset
of ) &
B
: ( ( ) ( )
Subset
of )
c=
D
: ( ( ) ( )
Subset
of ) holds
C1
: ( ( ) ( )
Subset
of )
=
C2
: ( ( ) ( )
Subset
of ) ;
theorem
:: JORDAN9:2
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
,
g
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st ( for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
|
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
=
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
|
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) holds
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
=
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ;
theorem
:: JORDAN9:3
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V26
() )
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
(
Rev
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V26
() )
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
(
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
/.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
=
(
Rev
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
theorem
:: JORDAN9:4
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) st
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
(
Rev
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V26
() )
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
V26
() )
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
=
(
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
(
Rev
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
/.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
=
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
2
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
b
2
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
begin
theorem
:: JORDAN9:5
for
D
being ( ( non
empty
) ( non
empty
)
set
)
for
G
being ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
Matrix
of ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )) )
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
D
: ( ( non
empty
) ( non
empty
)
set
) ) holds
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
is_sequence_on
G
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
Matrix
of ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )) ) iff
Rev
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
is_sequence_on
G
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
b
1
: ( ( non
empty
) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
Matrix
of ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) )) ) ) ;
theorem
:: JORDAN9:6
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
Matrix
of )
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
G
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
Matrix
of ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
Values
G
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
Matrix
of ) : ( ( ) (
V26
() )
set
) ;
theorem
:: JORDAN9:7
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
x
being ( ( ) ( )
set
) st
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
x
: ( ( ) ( )
set
)
in
L~
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/^
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) holds
ex
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
x
: ( ( ) ( )
set
)
in
LSeg
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
closed
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN9:8
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
left_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
right_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN9:9
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
Int
(
left_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
<>
{}
: ( ( ) ( )
set
) &
Int
(
right_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
<>
{}
: ( ( ) ( )
set
) ) ;
theorem
:: JORDAN9:10
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
Int
(
left_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
convex
&
Int
(
right_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
convex
) ;
theorem
:: JORDAN9:11
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
Cl
(
Int
(
left_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
=
left_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
Cl
(
Int
(
right_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
=
right_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN9:12
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) &
LSeg
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
closed
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
horizontal
holds
ex
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & ( for
p
being ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) ) st
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
LSeg
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
closed
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) holds
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) ) ) ) ;
theorem
:: JORDAN9:13
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) &
LSeg
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
closed
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) is
vertical
holds
ex
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & ( for
p
being ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) ) st
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
LSeg
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
closed
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) holds
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) ) ) ) ;
theorem
:: JORDAN9:14
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) &
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) is
special
&
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
Int
(
cell
(
G
: ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
misses
L~
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN9:15
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) &
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) is
special
& 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
Int
(
left_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
misses
L~
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
Int
(
right_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
misses
L~
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN9:16
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN9:17
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
p
being ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) iff (
(
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) )
<=
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) ) &
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) )
<=
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) ) &
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) ) ) ) ;
theorem
:: JORDAN9:18
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
=
{
|[
r
: ( ( ) (
V11
()
real
ext-real
)
Real
) ,
s
: ( ( ) (
V11
()
real
ext-real
)
Real
)
]|
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
Function-like
V26
() 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
FinSubsequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) where
r
,
s
is ( ( ) (
V11
()
real
ext-real
)
Real
) : (
(
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) )
<=
r
: ( ( ) (
V11
()
real
ext-real
)
Real
) &
r
: ( ( ) (
V11
()
real
ext-real
)
Real
)
<=
(
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) )
<=
s
: ( ( ) (
V11
()
real
ext-real
)
Real
) &
s
: ( ( ) (
V11
()
real
ext-real
)
Real
)
<=
(
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) ) )
}
;
theorem
:: JORDAN9:19
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
p
being ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
Values
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V26
() )
set
) &
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) & not
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( 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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) & not
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( 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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) & not
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( 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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) holds
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( 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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: JORDAN9:20
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN9:21
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
p
being ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
Values
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V26
() )
set
) &
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) holds
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
is_extremal_in
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN9:22
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
ex
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
LSeg
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
closed
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
c=
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN9:23
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
p
being ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) ) st 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) & 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
Values
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
V26
() )
set
) &
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
LSeg
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
closed
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) & not
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
=
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) holds
p
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Point
of ( ( ) ( non
empty
)
set
) )
=
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ;
theorem
:: JORDAN9:24
for
i
,
j
,
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st
[
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) ( )
set
) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
(
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) ) ;
theorem
:: JORDAN9:25
for
i
,
j
,
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) st
[
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) ( )
set
) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
*
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( )
set
) ) ;
theorem
:: JORDAN9:26
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
G
being ( ( non
empty-yielding
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
,
g
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) &
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) is
special
&
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
c=
L~
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
for
A
being ( ( ) ( )
Subset
of ) st (
A
: ( ( ) ( )
Subset
of )
=
(
right_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
\
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) or
A
: ( ( ) ( )
Subset
of )
=
(
left_cell
(
f
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
\
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) holds
A
: ( ( ) ( )
Subset
of ) is
connected
;
theorem
:: JORDAN9:27
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
)
for
f
being ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
is_sequence_on
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) holds
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
right_cell
(
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
\
(
L~
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
c=
RightComp
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
(
left_cell
(
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
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
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
Go-board
) )
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
\
(
L~
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
c=
LeftComp
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
begin
theorem
:: JORDAN9:28
for
C
being ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of )
for
n
being ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) ex
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
N-min
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
cell
(
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
N-min
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
<>
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) ;
theorem
:: JORDAN9:29
for
C
being ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of )
for
n
,
i1
,
i2
being ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i1
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) &
i1
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
)
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
N-min
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
cell
(
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i1
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) ,
(
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
N-min
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
<>
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i1
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) ,
(
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i2
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) &
i2
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
)
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
N-min
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
cell
(
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i2
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) ,
(
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
N-min
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
<>
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i2
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) ,
(
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) holds
i1
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
)
=
i2
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) ;
theorem
:: JORDAN9:30
for
C
being ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of )
for
n
being ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
)
for
f
being ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
is_sequence_on
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) ) : ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) & ( for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
left_cell
(
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
misses
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) &
right_cell
(
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
meets
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ) ) & ex
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) &
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) &
N-min
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
cell
(
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
N-min
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
<>
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
width
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) holds
N-min
(
L~
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
f
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ;
definition
let
C
be ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ;
let
n
be ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Nat
) ;
assume
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) is
connected
;
func
Cage
(
C
,
n
)
->
( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
means
:: JORDAN9:def 1
(
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) )
is_sequence_on
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) ) : ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) & ex
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) )
/.
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
width
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) &
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) )
/.
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
width
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) &
N-min
C
: ( ( ) ( )
RLTopStruct
) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
cell
(
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ,
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
width
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) &
N-min
C
: ( ( ) ( )
RLTopStruct
) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
<>
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
width
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) & ( for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
( (
front_left_cell
(
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
misses
C
: ( ( ) ( )
RLTopStruct
) &
front_right_cell
(
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
misses
C
: ( ( ) ( )
RLTopStruct
) implies
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) )
turns_right
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) ) : ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) & (
front_left_cell
(
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
misses
C
: ( ( ) ( )
RLTopStruct
) &
front_right_cell
(
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
meets
C
: ( ( ) ( )
RLTopStruct
) implies
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) )
goes_straight
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) ) : ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) & (
front_left_cell
(
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) ) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) )
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
meets
C
: ( ( ) ( )
RLTopStruct
) implies
it
: ( (
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) ) (
Relation-like
Function-like
V40
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) )
Element
of
K6
(
K7
(
K7
(
C
: ( ( ) ( )
RLTopStruct
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ,
C
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) (
Relation-like
)
set
) ) : ( ( ) ( )
set
) )
turns_left
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
Gauge
(
C
: ( ( ) ( )
RLTopStruct
) ,
n
: ( ( ) ( )
Element
of
C
: ( ( ) ( )
RLTopStruct
) ) ) : ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) ) ) );
end;
theorem
:: JORDAN9:31
for
k
,
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
C
being ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) st
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) is
connected
& 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) &
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
Cage
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
left_cell
(
(
Cage
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
misses
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) &
right_cell
(
(
Cage
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
) ,
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
Gauge
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
V26
()
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
*
: ( ( ) ( non
empty
functional
FinSequence-membered
)
M11
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
meets
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ) ;
theorem
:: JORDAN9:32
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
for
C
being ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) st
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) is
connected
holds
N-min
(
L~
(
Cage
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
closed
compact
)
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
Cage
(
C
: ( ( non
empty
compact
non
horizontal
non
vertical
) ( non
empty
compact
non
horizontal
non
vertical
)
Subset
of ) ,
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( non
empty
non
constant
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
) ( non
empty
V2
()
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
V26
()
FinSequence-like
FinSubsequence-like
V182
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
clockwise_oriented
)
special_circular_sequence
)
/.
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( 2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
-element
FinSequence-like
V86
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
ext-real
positive
non
negative
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
)
Element
of
K6
(
REAL
: ( ( ) ( )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V118
()
V143
()
V144
()
V145
()
V146
()
V147
()
V148
()
V149
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ;