begin
begin
begin
theorem
for
T being ( ( non
empty ) ( non
empty )
1-sorted )
for
F,
G being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of T : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
for
A being ( ( ) ( )
Subset of ) st
G : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) is ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
F : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) & ( for
i being ( (
natural ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Nat) holds
F : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( (
natural ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Nat) : ( ( ) ( )
set )
= A : ( ( ) ( )
Subset of ) ) holds
G : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= F : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ;
theorem
for
T being ( ( non
empty ) ( non
empty )
1-sorted )
for
S being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of T : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
for
R being ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
S : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
for
n being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) ex
m being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) st
(
m : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
>= n : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) &
R : ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
b2 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
. n : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= S : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. m : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty ) ( non
empty )
1-sorted ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty ) ( non empty ) 1-sorted ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ;
begin
theorem
for
T being ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace)
for
R,
S being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of T : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st
R : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) is ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
S : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) holds
Lim_inf S : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of )
c= Lim_inf R : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of ) ;
theorem
for
T being ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace)
for
A,
B being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of T : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
A : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
c= B : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) holds
Lim_inf A : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of )
c= Lim_inf B : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of ) ;
theorem
for
T being ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace)
for
A,
B,
C being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of T : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= (A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
\/ (B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
(Lim_inf A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
closed )
Subset of )
\/ (Lim_inf B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
closed )
Subset of ) : ( ( ) (
closed )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
c= Lim_inf C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of ) ;
theorem
for
T being ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace)
for
A,
B,
C being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of T : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= (A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
/\ (B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
Lim_inf C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of )
c= (Lim_inf A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
closed )
Subset of )
/\ (Lim_inf B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) (
closed )
Subset of ) : ( ( ) (
closed )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ;
theorem
for
T being ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace)
for
F,
G being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of T : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
G : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= Cl (F : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Element of
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
Lim_inf G : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of )
= Lim_inf F : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
b1 : ( ( non
empty TopSpace-like ) ( non
empty TopSpace-like )
TopSpace) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of b1 : ( ( non empty TopSpace-like ) ( non empty TopSpace-like ) TopSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of ) ;
theorem
for
n being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
for
S being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
for
p being ( ( ) (
Relation-like Function-like V37(
b1 : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) ) st ex
s being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) , the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) , the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) ) )
Real_Sequence of ) st
(
s : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) , the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) , the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) ) )
Real_Sequence of ) is
convergent & ( for
x being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
s : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) , the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) , the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) ) )
Real_Sequence of )
. x : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
Relation-like Function-like V37(
b1 : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Element of the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) )
in S : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. x : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) &
p : ( ( ) (
Relation-like Function-like V37(
b1 : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) )
= lim s : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) , the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) , the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) ) )
Real_Sequence of ) : ( ( ) (
Relation-like Function-like V37(
b1 : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Element of the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) ) ) holds
p : ( ( ) (
Relation-like Function-like V37(
b1 : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) )
FinSequence-like complex-valued ext-real-valued real-valued )
Point of ( ( ) ( non
empty )
set ) )
in Lim_inf S : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of ) ;
theorem
for
n being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
for
A,
B being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
for
C being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL n : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= [:(A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ,(B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) :] : ( ( ) (
Relation-like )
Element of
bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
[:(Lim_inf A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( closed ) Subset of ) ,(Lim_inf B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( closed ) Subset of ) :] : ( ( ) (
Relation-like )
Element of
bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
= Lim_inf C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL b1 : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Subset of ) ;
begin
theorem
for
A,
B,
C being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
A : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
b2 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
c= B : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
b2 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) &
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) is ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
A : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) holds
ex
D being ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
B : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) st
for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
c= D : ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
b2 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ;
theorem
for
A,
B,
C being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
A : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
b1 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
c= B : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
b1 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) &
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) is ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
B : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) holds
ex
D being ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
A : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) st
for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
D : ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
b1 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
c= C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ;
theorem
for
A,
B being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
A : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
c= B : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) holds
Lim_sup A : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Subset of )
c= Lim_sup B : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Subset of ) ;
theorem
for
A,
B,
C being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= (A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
\/ (B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
(Lim_sup A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Subset of )
\/ (Lim_sup B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Subset of ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
c= Lim_sup C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Subset of ) ;
theorem
for
A,
B,
C being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= (A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
/\ (B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
Lim_sup C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Subset of )
c= (Lim_sup A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Subset of )
/\ (Lim_sup B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Subset of ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ;
theorem
for
A,
B being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
for
C,
C1 being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= [:(A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ,(B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) :] : ( ( ) (
Relation-like )
Element of
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) &
C1 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) is ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) holds
ex
A1,
B1 being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st
(
A1 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) is ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
A : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) &
B1 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) is ( ( ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
subsequence of
B : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) & ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
C1 : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= [:(A1 : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ,(B1 : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) :] : ( ( ) (
Relation-like )
Element of
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ;
theorem
for
A,
B being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
for
C being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= [:(A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ,(B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) :] : ( ( ) (
Relation-like )
Element of
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
Lim_sup C : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of [:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( ( strict TopSpace-like ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Subset of )
c= [:(Lim_sup A : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Subset of ) ,(Lim_sup B : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( ) Subset of ) :] : ( ( ) (
Relation-like )
Element of
bool the
carrier of
[:(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) ,(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) :] : ( (
strict TopSpace-like ) ( non
empty strict TopSpace-like )
TopStruct ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ;
theorem
for
F,
G being ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) st ( for
i being ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
G : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
. i : ( ( ) (
epsilon-transitive epsilon-connected ordinal natural V11()
real integer ext-real non
negative )
Element of
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) )
= Cl (F : ( ( Function-like V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) ( non empty Relation-like NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) -defined bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) -valued Function-like V23( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) V27( NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) , bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) ) SetSequence of ( ( ) ( non empty ) Element of bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ) ) . i : ( ( ) ( epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( ) ( )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) (
closed )
Element of
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) holds
Lim_sup G : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Subset of )
= Lim_sup F : ( (
Function-like V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) ) ( non
empty Relation-like NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) )
-defined bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) )
-valued Function-like V23(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) )
V27(
NAT : ( ( ) ( non
empty epsilon-transitive epsilon-connected ordinal )
Element of
bool REAL : ( ( ) ( )
set ) : ( ( ) ( non
empty )
set ) ) ,
bool the
carrier of
(TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( (
strict ) ( non
empty TopSpace-like V126()
V194()
V195()
V212()
V213()
V214()
V215()
V216()
V217()
V218()
strict V225()
V226()
first-countable )
L16()) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) )
SetSequence of ( ( ) ( non
empty )
Element of
bool (bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal natural V11() real integer ext-real positive non negative ) Element of NAT : ( ( ) ( non empty epsilon-transitive epsilon-connected ordinal ) Element of bool REAL : ( ( ) ( ) set ) : ( ( ) ( non empty ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V126() V194() V195() V212() V213() V214() V215() V216() V217() V218() strict V225() V226() first-countable ) L16()) : ( ( ) ( non empty ) set ) ) : ( ( ) ( non
empty )
set ) : ( ( ) ( non
empty )
set ) ) ) : ( ( ) ( )
Subset of ) ;