:: JORDAN5D semantic presentation
begin
theorem
:: JORDAN5D:1
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
for
h
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) st
len
h
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
>=
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
h
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
(
len
h
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V42
(
b
1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
in
LSeg
(
h
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) ,
(
(
len
h
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
non
negative
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
b
1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ;
theorem
:: JORDAN5D:2
for
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 3 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
mod
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
-'
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
non
negative
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN5D:3
for
p
being ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) st
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
rng
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
trivial
finite
)
set
) holds
ex
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
)
=
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) ) ;
theorem
:: JORDAN5D:4
for
r
being ( ( ) (
V11
()
real
ext-real
)
Real
)
for
g
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
V89
()
V90
()
V91
() )
FinSequence
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) st
r
: ( ( ) (
V11
()
real
ext-real
)
Real
)
in
rng
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
V89
()
V90
()
V91
() )
FinSequence
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
finite
V99
()
V100
()
V101
()
bounded_below
bounded_above
real-bounded
)
set
) holds
(
(
Incr
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
V89
()
V90
()
V91
() )
FinSequence
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
)
: ( (
V93
() ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
one-to-one
finite
FinSequence-like
FinSubsequence-like
V89
()
V90
()
V91
()
V93
()
V95
() )
FinSequence
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
.
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V11
()
real
ext-real
)
set
)
<=
r
: ( ( ) (
V11
()
real
ext-real
)
Real
) &
r
: ( ( ) (
V11
()
real
ext-real
)
Real
)
<=
(
Incr
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
V89
()
V90
()
V91
() )
FinSequence
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
)
: ( (
V93
() ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
one-to-one
finite
FinSequence-like
FinSubsequence-like
V89
()
V90
()
V91
()
V93
()
V95
() )
FinSequence
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
.
(
len
(
Incr
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
V89
()
V90
()
V91
() )
FinSequence
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
)
: ( (
V93
() ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
one-to-one
finite
FinSequence-like
FinSubsequence-like
V89
()
V90
()
V91
()
V93
()
V95
() )
FinSequence
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V11
()
real
ext-real
)
set
) ) ;
theorem
:: JORDAN5D:5
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
,
I
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) ;
theorem
:: JORDAN5D:6
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
,
I
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) ;
theorem
:: JORDAN5D:7
for
f
being ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
ex
k
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
bounded_above
real-bounded
)
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
[
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) ;
theorem
:: JORDAN5D:8
for
f
being ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
ex
k
,
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
bounded_above
real-bounded
)
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
[
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) ;
theorem
:: JORDAN5D:9
for
f
being ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
bounded_above
real-bounded
)
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
[
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) ;
theorem
:: JORDAN5D:10
for
f
being ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
bounded_above
real-bounded
)
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
[
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) ;
begin
theorem
:: JORDAN5D:11
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
S-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
N-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) ;
theorem
:: JORDAN5D:12
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
W-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
E-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) ;
theorem
:: JORDAN5D:13
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
W-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
(
proj2
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
W-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
.:
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) : ( ( ) (
V99
()
V100
()
V101
() )
set
) ;
theorem
:: JORDAN5D:14
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
E-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
(
proj2
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
E-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
.:
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) : ( ( ) (
V99
()
V100
()
V101
() )
set
) ;
theorem
:: JORDAN5D:15
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
N-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
(
proj1
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
N-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
.:
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) : ( ( ) (
V99
()
V100
()
V101
() )
set
) ;
theorem
:: JORDAN5D:16
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
S-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
(
proj1
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
S-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
.:
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) : ( ( ) (
V99
()
V100
()
V101
() )
set
) ;
theorem
:: JORDAN5D:17
for
g
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) :
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
}
holds
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
(
proj1
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
.:
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) : ( ( ) (
V99
()
V100
()
V101
() )
set
) ;
theorem
:: JORDAN5D:18
for
g
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) :
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
}
holds
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
(
proj2
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
.:
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) : ( ( ) (
V99
()
V100
()
V101
() )
set
) ;
theorem
:: JORDAN5D:19
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
W-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
lower_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
lower_bound
(
proj2
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
W-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:20
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
W-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
upper_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
upper_bound
(
proj2
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
W-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
W-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:21
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
E-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
lower_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
lower_bound
(
proj2
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
E-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:22
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
E-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
upper_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
upper_bound
(
proj2
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
E-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
E-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:23
for
g
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) :
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
}
holds
lower_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
lower_bound
(
proj1
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:24
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
S-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
lower_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
lower_bound
(
proj1
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
S-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:25
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
S-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
upper_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
upper_bound
(
proj1
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
S-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
S-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:26
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
N-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
lower_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
lower_bound
(
proj1
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
N-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:27
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) : (
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
N-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) )
}
holds
upper_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
upper_bound
(
proj1
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
N-most
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
N-most
(
L~
b
1
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
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
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:28
for
g
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) :
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
}
holds
lower_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
lower_bound
(
proj2
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:29
for
g
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) :
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
}
holds
upper_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
upper_bound
(
proj1
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:30
for
g
being ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
X
being ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) )
=
{
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
)
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) where
q
is ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) :
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
}
holds
upper_bound
X
: ( ( ) (
V99
()
V100
()
V101
() )
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
upper_bound
(
proj2
: ( (
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) )
|
(
L~
g
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ) (
Relation-like
the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
)
-defined
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
)
-valued
Function-like
V29
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
V89
()
V90
()
V91
() )
Element
of
K6
(
K7
( the
carrier
of
(
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
)
|
(
L~
b
1
: ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( ( ) (
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) )
)
: ( (
strict
) (
strict
)
SubSpace
of
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) : ( ( ) ( )
set
) ,
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) (
V89
()
V90
()
V91
() )
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:31
for
p
being ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
I
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:32
for
p
being ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
I
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:33
for
p
being ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
I
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:34
for
p
being ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
I
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
p
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:35
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
ex
q
being ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) st
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN5D:36
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
,
j
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
ex
q
being ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) ) st
(
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
q
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Point
of ( ( ) ( non
empty
)
set
) )
in
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN5D:37
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
W-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:38
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
S-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:39
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
E-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:40
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
N-bound
(
L~
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( ( ) ( non
empty
V85
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) ) )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:41
for
f
being ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
i
,
I
,
i1
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
for
Y
being ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
Y
: ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) )
=
{
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) where
j
is ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : (
[
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) & ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
bounded_above
real-bounded
)
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) )
}
&
(
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
i1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
=
min
Y
: ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
i1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:42
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
,
I
,
i1
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
for
Y
being ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
Y
: ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) )
=
{
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) where
j
is ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : (
[
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) & ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
trivial
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
bounded_above
real-bounded
)
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) )
}
&
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
i1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
=
min
Y
: ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
<=
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:43
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
for
i
,
I
,
i1
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
for
Y
being ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
Y
: ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) )
=
{
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) where
j
is ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : (
[
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) & ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) ( non
trivial
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
bounded_above
real-bounded
)
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) )
}
&
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
i1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
=
max
Y
: ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) ) : ( (
ext-real
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
)
set
) holds
(
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
i1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
>=
(
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
theorem
:: JORDAN5D:44
for
f
being ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
for
i
,
I
,
i1
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
for
Y
being ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) ) st 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
Y
: ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) )
=
{
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) where
j
is ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : (
[
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) & ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
in
dom
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) ) : ( ( ) (
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
bounded_above
real-bounded
)
Element
of
K6
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
j
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) ) )
}
&
(
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
=
(
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`1
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) &
i1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
=
max
Y
: ( ( non
empty
finite
) ( non
empty
finite
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
right_end
bounded_below
bounded_above
real-bounded
)
Subset
of ( ( ) ( )
set
) ) : ( (
ext-real
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
)
set
) holds
(
(
GoB
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
I
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
i1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) )
>=
(
f
: ( ( non
empty
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
)
FinSequence
of ( ( ) ( non
empty
)
set
) )
/.
i
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
`2
: ( ( ) (
V11
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) ;
begin
definition
let
g
be ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ;
func
i_s_w
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 1
(
[
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
W-min
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
i_n_w
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 2
(
[
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
W-max
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
i_s_e
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 3
(
[
(
len
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
len
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
E-min
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
i_n_e
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 4
(
[
(
len
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
(
len
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
E-max
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
i_w_s
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 5
(
[
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
S-min
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
i_e_s
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 6
(
[
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
S-max
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
i_w_n
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 7
(
[
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ,
(
width
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ,
(
width
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
N-min
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
i_e_n
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 8
(
[
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ,
(
width
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
]
: ( ( ) ( )
set
)
in
Indices
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) ( )
set
) &
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
*
(
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) ,
(
width
(
GoB
g
: ( ( ) ( )
RLTopStruct
)
)
: ( (
tabular
) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
=
N-max
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
end;
theorem
:: JORDAN5D:45
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i_w_n
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i_w_n
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i_e_n
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i_e_n
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i_w_s
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i_w_s
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i_e_s
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i_e_s
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) ;
theorem
:: JORDAN5D:46
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i_n_e
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i_n_e
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i_s_e
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i_s_e
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i_n_w
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i_n_w
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) & 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
i_s_w
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
i_s_w
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
width
(
GoB
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
)
)
: ( (
tabular
) (
Relation-like
non
empty-yielding
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ))
-valued
Function-like
finite
FinSequence-like
FinSubsequence-like
tabular
X_equal-in-line
Y_equal-in-column
Y_increasing-in-line
X_increasing-in-column
)
FinSequence
of
K266
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( non
empty
functional
FinSequence-membered
)
M8
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ) ;
definition
let
g
be ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) ;
func
n_s_w
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 9
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) &
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
g
: ( ( ) ( )
RLTopStruct
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
g
: ( ( ) ( )
RLTopStruct
)
.
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) ( )
set
)
=
W-min
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
n_n_w
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 10
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) &
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
g
: ( ( ) ( )
RLTopStruct
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
g
: ( ( ) ( )
RLTopStruct
)
.
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) ( )
set
)
=
W-max
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
n_s_e
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 11
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) &
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
g
: ( ( ) ( )
RLTopStruct
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
g
: ( ( ) ( )
RLTopStruct
)
.
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) ( )
set
)
=
E-min
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
n_n_e
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 12
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) &
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
g
: ( ( ) ( )
RLTopStruct
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
g
: ( ( ) ( )
RLTopStruct
)
.
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) ( )
set
)
=
E-max
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
n_w_s
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 13
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) &
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
g
: ( ( ) ( )
RLTopStruct
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
g
: ( ( ) ( )
RLTopStruct
)
.
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) ( )
set
)
=
S-min
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
n_e_s
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 14
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) &
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
g
: ( ( ) ( )
RLTopStruct
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
g
: ( ( ) ( )
RLTopStruct
)
.
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) ( )
set
)
=
S-max
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
n_w_n
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 15
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) &
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
g
: ( ( ) ( )
RLTopStruct
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
g
: ( ( ) ( )
RLTopStruct
)
.
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) ( )
set
)
=
N-min
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
func
n_e_n
g
->
( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
means
:: JORDAN5D:def 16
( 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) &
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<=
len
g
: ( ( ) ( )
RLTopStruct
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) &
g
: ( ( ) ( )
RLTopStruct
)
.
it
: ( ( ) ( )
Element
of
g
: ( ( ) ( )
RLTopStruct
) ) : ( ( ) ( )
set
)
=
N-max
(
L~
g
: ( ( ) ( )
RLTopStruct
)
)
: ( ( ) ( )
Element
of
K6
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) : ( ( ) ( )
set
) ) : ( ( ) (
V42
(2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) )
FinSequence-like
V91
() )
Element
of the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) ) );
end;
theorem
:: JORDAN5D:47
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
n_w_n
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<>
n_w_s
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN5D:48
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
n_s_w
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<>
n_s_e
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN5D:49
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
n_e_n
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<>
n_e_s
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: JORDAN5D:50
for
h
being ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) holds
n_n_w
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
<>
n_n_e
h
: ( ( non
empty
non
constant
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
) ( non
empty
non
trivial
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) )
-defined
the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
)
-valued
Function-like
non
constant
finite
FinSequence-like
FinSubsequence-like
V186
( the
carrier
of
(
TOP-REAL
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
positive
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
left_end
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( (
strict
) ( non
empty
TopSpace-like
V137
()
V162
()
V163
()
V164
()
V165
()
V166
()
V167
()
V168
()
strict
)
RLTopStruct
) : ( ( ) ( non
empty
)
set
) )
special
unfolded
s.c.c.
standard
)
special_circular_sequence
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V11
()
real
V13
()
V32
()
ext-real
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
bounded_below
)
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V99
()
V100
()
V101
()
V102
()
V103
()
V104
()
V105
()
left_end
bounded_below
)
Element
of
K6
(
REAL
: ( ( ) ( non
empty
non
trivial
non
finite
V99
()
V100
()
V101
()
V105
() non
bounded_below
non
bounded_above
V204
() )
set
) ) : ( ( ) ( )
set
) ) ) ;