:: BOR_CANT semantic presentation
begin
definition
let
D
be ( ( ) ( )
set
) ;
let
x
,
y
be ( (
ext-real
) (
ext-real
)
number
) ;
let
a
,
b
be ( ( ) ( )
Element
of
D
: ( ( ) ( )
set
) ) ;
:: original:
IFGT
redefine
func
IFGT
(
x
,
y
,
a
,
b
)
->
( ( ) ( )
Element
of
D
: ( (
V28
() ) (
V28
() )
set
) ) ;
end;
theorem
:: BOR_CANT:1
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
for
x
being ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) st
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) is
odd
&
x
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
>
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
x
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
<=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
(
(
(
-
x
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
rExpSeq
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
+
(
(
(
-
x
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
rExpSeq
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
2 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
>=
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
theorem
:: BOR_CANT:2
for
x
being ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) holds 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
x
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
<=
exp_R
: ( (
Function-like
V18
(
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V18
(
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
x
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
definition
let
s
be ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Real_Sequence
) ;
func
JSum
s
->
( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Real_Sequence
)
means
:: BOR_CANT:def 1
for
d
being ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
ext-real
non
negative
)
Nat
) holds
it
: ( ( ) (
V28
() )
Element
of
COMPLEX
: ( ( ) ( non
empty
V34
()
V70
()
V76
() )
set
) )
.
d
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
ext-real
non
negative
)
Nat
) : ( ( ) ( )
set
)
=
Sum
(
(
-
(
s
: ( (
V28
() ) (
V28
() )
set
)
.
d
: ( (
natural
) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
ext-real
non
negative
)
Nat
)
)
: ( ( ) ( )
set
)
)
: ( (
V28
() ) (
V28
() )
set
)
rExpSeq
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
end;
theorem
:: BOR_CANT:3
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
(
Partial_Product
(
JSum
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Real_Sequence
)
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
exp_R
: ( (
Function-like
V18
(
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V18
(
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
(
-
(
(
Partial_Sums
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
theorem
:: BOR_CANT:4
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
(
Partial_Product
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
<=
(
Partial_Product
(
JSum
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Real_Sequence
)
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
definition
let
n1
,
n2
be ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
func
Special_Function
(
n1
,
n2
)
->
( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
means
:: BOR_CANT:def 2
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
it
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
=
IFGT
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
n1
: ( (
V28
() ) (
V28
() )
set
) ,
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
n2
: ( ( ) (
V28
() )
Element
of
COMPLEX
: ( ( ) ( non
empty
V34
()
V70
()
V76
() )
set
) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
end;
definition
let
k
be ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
func
Special_Function2
k
->
( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
means
:: BOR_CANT:def 3
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
it
: ( ( ) (
V28
() )
Element
of
COMPLEX
: ( ( ) ( non
empty
V34
()
V70
()
V76
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
=
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
k
: ( (
V28
() ) (
V28
() )
set
) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
end;
definition
let
k
be ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
func
Special_Function3
k
->
( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
means
:: BOR_CANT:def 4
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
it
: ( ( ) (
V28
() )
Element
of
COMPLEX
: ( ( ) ( non
empty
V34
()
V70
()
V76
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
=
IFGT
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
k
: ( (
V28
() ) (
V28
() )
set
) ,
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
end;
definition
let
n1
,
n2
be ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
func
Special_Function4
(
n1
,
n2
)
->
( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
means
:: BOR_CANT:def 5
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
it
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
=
IFGT
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
(
n1
: ( (
V28
() ) (
V28
() )
set
)
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
n2
: ( ( ) (
V28
() )
Element
of
COMPLEX
: ( ( ) ( non
empty
V34
()
V70
()
V76
() )
set
) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) : ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
end;
registration
let
n1
,
n2
be ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
cluster
Special_Function
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
n2
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
->
Function-like
one-to-one
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
cluster
Special_Function4
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
n2
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
->
Function-like
one-to-one
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
end;
registration
let
n
be ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
cluster
Special_Function2
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
->
Function-like
one-to-one
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
end;
registration
let
Omega
be ( ( non
empty
) ( non
empty
)
set
) ;
let
Sigma
be ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ;
let
s
be ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
let
A
be ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
cluster
A
: ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
^\
s
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
set
)
->
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
end;
theorem
:: BOR_CANT:5
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
,
n1
,
n2
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
( ( for
A
,
B
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) st
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
>
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
B
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
=
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
(
Special_Function
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
n2
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
one-to-one
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( (
Function-like
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) holds
(
Partial_Product
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
B
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
(
(
Partial_Product
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
*
(
(
Partial_Product
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
(
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
^\
(
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
n2
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
M16
(
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
b
7
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ))
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
(
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
-
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
-
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
set
) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) & ( for
A
,
B
,
C
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
e
being ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
>
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
C
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
=
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
e
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( (
Function-like
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) &
B
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
=
C
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
(
Special_Function
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ,
n2
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
one-to-one
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( (
Function-like
) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) holds
(
Partial_Intersection
B
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
=
(
(
Partial_Intersection
C
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
/\
(
(
Partial_Intersection
(
C
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
^\
(
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
n2
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
M16
(
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
b
9
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ))
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
(
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
-
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
-
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
)
: ( ( ) ( )
set
) : ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ;
definition
let
Omega
be ( ( non
empty
) ( non
empty
)
set
) ;
let
Sigma
be ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ;
let
Prob
be ( ( ) ( non
empty
Relation-like
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
let
A
be ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
pred
A
is_all_independent_wrt
Prob
means
:: BOR_CANT:def 6
for
B
being ( (
Sigma
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( ) ( )
set
) ) st ex
e
being ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V59
()
V60
()
V61
()
V62
() )
sequence
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
(
e
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) is
one-to-one
& ( for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
A
: ( (
Sigma
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
(
e
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
Sigma
: ( ( ) ( )
set
) )
=
B
: ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
Sigma
: ( ( ) ( )
set
) ) ) ) holds
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
(
Partial_Product
(
Prob
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
*
B
: ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
Prob
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
.
(
(
Partial_Intersection
B
: ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
Sigma
: ( ( ) ( )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
end;
theorem
:: BOR_CANT:6
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
,
n1
,
n2
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
>
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
is_all_independent_wrt
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) holds
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
(
(
Partial_Intersection
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
/\
(
(
Partial_Intersection
(
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
^\
(
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
n2
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
M16
(
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
b
4
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ))
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
(
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
-
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
-
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
)
: ( ( ) ( )
set
)
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
(
(
Partial_Product
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
*
(
(
Partial_Product
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
(
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
^\
(
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
n2
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
M16
(
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
b
4
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ))
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
(
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
-
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
-
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
set
) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
theorem
:: BOR_CANT:7
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
(
Partial_Intersection
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
=
(
(
Partial_Union
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
`
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ;
theorem
:: BOR_CANT:8
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
(
Partial_Intersection
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
-
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
(
Partial_Union
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
definition
let
X
be ( ( ) ( )
set
) ;
let
A
be ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
func
Union_Shift_Seq
A
->
( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
means
:: BOR_CANT:def 7
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
it
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Element
of
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
=
Union
(
A
: ( ( ) ( )
set
)
^\
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
M16
(
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
A
: ( ( ) ( )
set
) )) : ( ( ) ( )
Element
of
bool
X
: ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) ) ;
end;
registration
let
Omega
be ( ( non
empty
) ( non
empty
)
set
) ;
let
Sigma
be ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ;
let
A
be ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
cluster
Union_Shift_Seq
A
: ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
->
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
end;
definition
let
Omega
be ( ( non
empty
) ( non
empty
)
set
) ;
let
Sigma
be ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ;
let
A
be ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
func
@lim_sup
A
->
( ( ) ( )
Event
of
Sigma
: ( ( ) ( )
set
) )
equals
:: BOR_CANT:def 8
@Intersection
(
Union_Shift_Seq
A
: ( (
Sigma
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
Sigma
: ( ( ) ( )
set
) ) ;
end;
definition
let
X
be ( ( ) ( )
set
) ;
let
A
be ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
func
Intersect_Shift_Seq
A
->
( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
means
:: BOR_CANT:def 9
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
it
: ( (
A
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
A
: ( ( ) ( )
set
)
-valued
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Element
of
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
=
Intersection
(
A
: ( ( ) ( )
set
)
^\
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
M16
(
K496
(
X
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
A
: ( ( ) ( )
set
) )) : ( ( ) ( )
Element
of
bool
X
: ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) ) ;
end;
registration
let
Omega
be ( ( non
empty
) ( non
empty
)
set
) ;
let
Sigma
be ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ;
let
A
be ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
cluster
Intersect_Shift_Seq
A
: ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
->
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ;
end;
definition
let
Omega
be ( ( non
empty
) ( non
empty
)
set
) ;
let
Sigma
be ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ;
let
A
be ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
func
@lim_inf
A
->
( ( ) ( )
Event
of
Sigma
: ( ( ) ( )
set
) )
equals
:: BOR_CANT:def 10
Union
(
Intersect_Shift_Seq
A
: ( (
Sigma
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Element
of
bool
Omega
: ( ( ) ( )
set
) : ( ( ) ( non
empty
)
set
) ) ;
end;
theorem
:: BOR_CANT:9
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
(
Intersect_Shift_Seq
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
=
(
(
Union_Shift_Seq
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
`
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ;
theorem
:: BOR_CANT:10
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
is_all_independent_wrt
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) holds
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
(
Partial_Intersection
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
(
Partial_Product
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
theorem
:: BOR_CANT:11
for
X
being ( ( ) ( )
set
)
for
A
being ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
X
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
(
superior_setsequence
A
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
non-ascending
)
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
=
Union_Shift_Seq
A
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
inferior_setsequence
A
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
non-descending
)
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
=
Intersect_Shift_Seq
A
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
)
Element
of
bool
(
bool
b
1
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ;
theorem
:: BOR_CANT:12
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) holds
(
superior_setsequence
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
non-ascending
)
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
=
Union_Shift_Seq
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
inferior_setsequence
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
non-descending
)
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
=
Intersect_Shift_Seq
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ;
definition
let
Omega
be ( ( non
empty
) ( non
empty
)
set
) ;
let
Sigma
be ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ;
let
Prob
be ( ( ) ( non
empty
Relation-like
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
let
A
be ( (
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
Omega
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) ) ;
func
Sum_Shift_Seq
(
Prob
,
A
)
->
( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Real_Sequence
)
means
:: BOR_CANT:def 11
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
it
: ( (
Function-like
) (
Relation-like
Omega
: ( ( ) ( )
set
)
-defined
Prob
: ( (
Sigma
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V59
()
V60
()
V61
() )
Element
of
bool
[:
Omega
: ( ( ) ( )
set
) ,
Prob
: ( (
Sigma
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) (
Relation-like
)
set
) : ( ( ) ( non
empty
)
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
Sum
(
Prob
: ( (
Sigma
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
*
(
A
: ( (
Sigma
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
^\
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
M16
(
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
A
: ( (
Sigma
: ( ( ) ( )
set
)
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
Omega
: ( ( ) ( )
set
) ) : ( ( ) ( non
empty
)
Element
of
bool
(
bool
Omega
: ( ( ) ( )
set
)
)
: ( ( ) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ))
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
Sigma
: ( ( ) ( )
set
)
-valued
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
end;
theorem
:: BOR_CANT:13
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) st
Partial_Sums
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) is
convergent
holds
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
@lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
lim
(
Sum_Shift_Seq
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ,
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Real_Sequence
) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
Sum_Shift_Seq
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ,
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Real_Sequence
) is
convergent
) ;
theorem
:: BOR_CANT:14
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) holds
( ( for
X
being ( ( ) ( )
set
)
for
A
being ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
X
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
for
x
being ( ( ) ( )
set
) holds
( ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
x
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
in
(
A
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
^\
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
M16
(
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
b
4
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ))
.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
)
Element
of
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) iff ex
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
(
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
>=
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
x
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
in
A
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
)
Element
of
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ) ) & ( for
X
being ( ( ) ( )
set
)
for
A
being ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
X
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
for
x
being ( ( ) ( )
set
) holds
(
x
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
in
Intersection
(
Union_Shift_Seq
A
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
)
Element
of
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
V94
() )
set
) ) iff for
m
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ex
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
>=
m
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
x
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
in
A
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
)
Element
of
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ) ) & ( for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
x
being ( ( ) ( )
set
) holds
(
x
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
@Intersection
(
Union_Shift_Seq
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) iff for
m
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ex
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
(
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
>=
m
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
x
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) ) ) & ( for
X
being ( ( ) ( )
set
)
for
A
being ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
X
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
for
x
being ( ( ) ( )
set
) holds
(
x
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
in
Union
(
Intersect_Shift_Seq
A
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
)
Element
of
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) ( non
empty
V94
() )
set
) ) iff ex
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
>=
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
x
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
in
A
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
)
Element
of
K496
(
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
3
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ) & ( for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
x
being ( ( ) ( )
set
) holds
(
x
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
Union
(
Intersect_Shift_Seq
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) iff ex
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
>=
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
x
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) ) & ( for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
x
being ( ( ) ( )
Element
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) ) holds
(
x
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
Union
(
Intersect_Shift_Seq
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) iff ex
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
for
k
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) st
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
>=
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
not
x
: ( ( ) ( )
Element
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
in
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
k
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ) ) ) ;
theorem
:: BOR_CANT:15
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) holds
(
lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
=
@lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) &
lim_inf
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
=
@lim_inf
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) &
@lim_inf
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
=
(
@lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
`
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) &
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
@lim_inf
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
+
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
@lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_inf
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
set
)
+
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( ( ) (
V28
()
real
ext-real
)
set
) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ;
theorem
:: BOR_CANT:16
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) holds
( (
Partial_Sums
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) is
convergent
implies (
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_inf
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ) & (
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
is_all_independent_wrt
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) &
Partial_Sums
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) is
divergent_to+infty
implies (
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_inf
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ) ) ;
theorem
:: BOR_CANT:17
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) st not
Partial_Sums
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) is
convergent
&
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
is_all_independent_wrt
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) holds
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_inf
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) &
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ;
theorem
:: BOR_CANT:18
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) st
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
is_all_independent_wrt
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) holds
( (
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_inf
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) or
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_inf
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) & (
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
0
: ( ( ) (
empty
Relation-like
non-empty
empty-yielding
RAT
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V73
()
V76
() )
set
)
-valued
functional
epsilon-transitive
epsilon-connected
ordinal
T-Sequence-like
c=-linear
natural
V28
()
real
V30
()
V31
()
V42
()
V44
()
ext-real
non
positive
non
negative
V59
()
V60
()
V61
()
V62
()
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) or
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
lim_sup
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) ( )
Element
of
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
) : ( ( ) ( non
empty
V94
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
set
)
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ) ;
theorem
:: BOR_CANT:19
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n1
,
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
(
Partial_Sums
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
(
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
^\
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
M16
(
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
b
4
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) ))
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
<=
(
(
Partial_Sums
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
(
(
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
+
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
-
(
(
Partial_Sums
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n1
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
theorem
:: BOR_CANT:20
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
(
Intersect_Shift_Seq
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
-
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
(
Union_Shift_Seq
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ;
theorem
:: BOR_CANT:21
for
Omega
being ( ( non
empty
) ( non
empty
)
set
)
for
Sigma
being ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
Omega
: ( ( non
empty
) ( non
empty
)
set
) )
for
Prob
being ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
A
being ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
Sigma
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
for
n
being ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) holds
( (
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
is_all_independent_wrt
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) implies
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
(
Partial_Intersection
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
(
Partial_Product
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) & (
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
is_all_independent_wrt
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ) implies 1 : ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
positive
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
-
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
.
(
(
Partial_Union
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
)
: ( ( ) ( )
Event
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
=
(
Partial_Product
(
Prob
: ( ( ) ( non
empty
Relation-like
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
V18
(
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Probability
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
*
(
Complement
A
: ( (
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
SetSequence
of
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
b
2
: ( ( non
empty
compl-closed
sigma-multiplicative
) ( non
empty
compl-closed
sigma-multiplicative
)
SigmaField
of
b
1
: ( ( non
empty
) ( non
empty
)
set
) )
-valued
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
K496
(
b
1
: ( ( non
empty
) ( non
empty
)
set
) ) : ( ( ) ( non
empty
V94
() )
Element
of
bool
(
bool
b
1
: ( ( non
empty
) ( non
empty
)
set
)
)
: ( ( ) ( non
empty
V94
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
:]
: ( ( ) ( non
empty
Relation-like
)
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
)
: ( (
Function-like
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ( non
empty
Relation-like
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
-defined
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
-valued
Function-like
V17
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) )
V18
(
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) )
V59
()
V60
()
V61
() )
Element
of
bool
[:
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ,
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
)
:]
: ( ( ) ( non
empty
Relation-like
V59
()
V60
()
V61
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) )
.
n
: ( ( ) (
epsilon-transitive
epsilon-connected
ordinal
natural
V28
()
real
V30
()
V31
()
ext-real
non
negative
V70
()
V71
()
V72
()
V73
()
V74
()
V75
() )
Element
of
NAT
: ( ( ) ( non
empty
epsilon-transitive
epsilon-connected
ordinal
V70
()
V71
()
V72
()
V73
()
V74
()
V75
()
V76
() )
Element
of
bool
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) : ( ( ) ( non
empty
V94
() )
set
) ) ) : ( ( ) (
V28
()
real
ext-real
)
Element
of
REAL
: ( ( ) ( non
empty
V34
()
V70
()
V71
()
V72
()
V76
() )
set
) ) ) ) ;